diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index da939687500b6..b647b8cff2058 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -158,6 +158,7 @@ Other enhancements
 - :meth:`DataFrame.describe` now formats integer percentiles without decimal point (:issue:`26660`)
 - Added support for reading SPSS .sav files using :func:`read_spss` (:issue:`26537`)
 - Added new option ``plotting.backend`` to be able to select a plotting backend different than the existing ``matplotlib`` one. Use ``pandas.set_option('plotting.backend', '<backend-module>')`` where ``<backend-module`` is a library implementing the pandas plotting API (:issue:`14130`)
+- :class:`pandas.offsets.BusinessHour` supports multiple opening hours intervals (:issue:`15481`)
 
 .. _whatsnew_0250.api_breaking:
 
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 5683924ee1283..c0021b1eade78 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -1,4 +1,4 @@
-from datetime import date, datetime, timedelta
+from datetime import date, datetime, time as dt_time, timedelta
 
 import numpy as np
 import pytest
@@ -759,15 +759,66 @@ def setup_method(self, method):
         self.offset6 = BusinessHour(start='20:00', end='05:00')
         self.offset7 = BusinessHour(n=-2, start=dt_time(21, 30),
                                     end=dt_time(6, 30))
-
-    def test_constructor_errors(self):
-        from datetime import time as dt_time
-        with pytest.raises(ValueError):
-            BusinessHour(start=dt_time(11, 0, 5))
-        with pytest.raises(ValueError):
-            BusinessHour(start='AAA')
-        with pytest.raises(ValueError):
-            BusinessHour(start='14:00:05')
+        self.offset8 = BusinessHour(start=['09:00', '13:00'],
+                                    end=['12:00', '17:00'])
+        self.offset9 = BusinessHour(n=3, start=['09:00', '22:00'],
+                                    end=['13:00', '03:00'])
+        self.offset10 = BusinessHour(n=-1, start=['23:00', '13:00'],
+                                     end=['02:00', '17:00'])
+
+    @pytest.mark.parametrize("start,end,match", [
+        (
+            dt_time(11, 0, 5),
+            '17:00',
+            "time data must be specified only with hour and minute"
+        ),
+        (
+            'AAA',
+            '17:00',
+            "time data must match '%H:%M' format"
+        ),
+        (
+            '14:00:05',
+            '17:00',
+            "time data must match '%H:%M' format"
+        ),
+        (
+            [],
+            '17:00',
+            "Must include at least 1 start time"
+        ),
+        (
+            '09:00',
+            [],
+            "Must include at least 1 end time"
+        ),
+        (
+            ['09:00', '11:00'],
+            '17:00',
+            "number of starting time and ending time must be the same"
+        ),
+        (
+            ['09:00', '11:00'],
+            ['10:00'],
+            "number of starting time and ending time must be the same"
+        ),
+        (
+            ['09:00', '11:00'],
+            ['12:00', '20:00'],
+            r"invalid starting and ending time\(s\): opening hours should not "
+            "touch or overlap with one another"
+        ),
+        (
+            ['12:00', '20:00'],
+            ['09:00', '11:00'],
+            r"invalid starting and ending time\(s\): opening hours should not "
+            "touch or overlap with one another"
+        ),
+    ])
+    def test_constructor_errors(self, start, end, match):
+        with pytest.raises(ValueError,
+                           match=match):
+            BusinessHour(start=start, end=end)
 
     def test_different_normalize_equals(self):
         # GH#21404 changed __eq__ to return False when `normalize` doesnt match
@@ -784,6 +835,12 @@ def test_repr(self):
         assert repr(self.offset5) == '<BusinessHour: BH=11:00-14:30>'
         assert repr(self.offset6) == '<BusinessHour: BH=20:00-05:00>'
         assert repr(self.offset7) == '<-2 * BusinessHours: BH=21:30-06:30>'
+        assert (repr(self.offset8) ==
+                '<BusinessHour: BH=09:00-12:00,13:00-17:00>')
+        assert (repr(self.offset9) ==
+                '<3 * BusinessHours: BH=09:00-13:00,22:00-03:00>')
+        assert (repr(self.offset10) ==
+                '<-1 * BusinessHour: BH=13:00-17:00,23:00-02:00>')
 
     def test_with_offset(self):
         expected = Timestamp('2014-07-01 13:00')
@@ -791,25 +848,59 @@ def test_with_offset(self):
         assert self.d + BusinessHour() * 3 == expected
         assert self.d + BusinessHour(n=3) == expected
 
-    def test_eq(self):
-        for offset in [self.offset1, self.offset2, self.offset3, self.offset4]:
-            assert offset == offset
+    @pytest.mark.parametrize("offset_name", [
+        "offset1",
+        "offset2",
+        "offset3",
+        "offset4",
+        "offset8",
+        "offset9",
+        "offset10"
+    ])
+    def test_eq_attribute(self, offset_name):
+        offset = getattr(self, offset_name)
+        assert offset == offset
+
+    @pytest.mark.parametrize("offset1,offset2", [
+        (BusinessHour(start='09:00'), BusinessHour()),
+        (BusinessHour(start=['23:00', '13:00'], end=['12:00', '17:00']),
+         BusinessHour(start=['13:00', '23:00'], end=['17:00', '12:00'])),
+    ])
+    def test_eq(self, offset1, offset2):
+        assert offset1 == offset2
 
-        assert BusinessHour() != BusinessHour(-1)
-        assert BusinessHour(start='09:00') == BusinessHour()
-        assert BusinessHour(start='09:00') != BusinessHour(start='09:01')
-        assert (BusinessHour(start='09:00', end='17:00') !=
-                BusinessHour(start='17:00', end='09:01'))
+    @pytest.mark.parametrize("offset1,offset2", [
+        (BusinessHour(), BusinessHour(-1)),
+        (BusinessHour(start='09:00'), BusinessHour(start='09:01')),
+        (BusinessHour(start='09:00', end='17:00'),
+         BusinessHour(start='17:00', end='09:01')),
+        (BusinessHour(start=['13:00', '23:00'], end=['18:00', '07:00']),
+         BusinessHour(start=['13:00', '23:00'], end=['17:00', '12:00'])),
+    ])
+    def test_neq(self, offset1, offset2):
+        assert offset1 != offset2
 
-    def test_hash(self):
-        for offset in [self.offset1, self.offset2, self.offset3, self.offset4]:
-            assert hash(offset) == hash(offset)
+    @pytest.mark.parametrize("offset_name", [
+        "offset1",
+        "offset2",
+        "offset3",
+        "offset4",
+        "offset8",
+        "offset9",
+        "offset10"
+    ])
+    def test_hash(self, offset_name):
+        offset = getattr(self, offset_name)
+        assert offset == offset
 
     def test_call(self):
         assert self.offset1(self.d) == datetime(2014, 7, 1, 11)
         assert self.offset2(self.d) == datetime(2014, 7, 1, 13)
         assert self.offset3(self.d) == datetime(2014, 6, 30, 17)
         assert self.offset4(self.d) == datetime(2014, 6, 30, 14)
+        assert self.offset8(self.d) == datetime(2014, 7, 1, 11)
+        assert self.offset9(self.d) == datetime(2014, 7, 1, 22)
+        assert self.offset10(self.d) == datetime(2014, 7, 1, 1)
 
     def test_sub(self):
         # we have to override test_sub here because self.offset2 is not
@@ -830,6 +921,9 @@ def testRollback1(self):
         assert self.offset5.rollback(self.d) == datetime(2014, 6, 30, 14, 30)
         assert self.offset6.rollback(self.d) == datetime(2014, 7, 1, 5, 0)
         assert self.offset7.rollback(self.d) == datetime(2014, 7, 1, 6, 30)
+        assert self.offset8.rollback(self.d) == self.d
+        assert self.offset9.rollback(self.d) == self.d
+        assert self.offset10.rollback(self.d) == datetime(2014, 7, 1, 2)
 
         d = datetime(2014, 7, 1, 0)
         assert self.offset1.rollback(d) == datetime(2014, 6, 30, 17)
@@ -839,6 +933,9 @@ def testRollback1(self):
         assert self.offset5.rollback(d) == datetime(2014, 6, 30, 14, 30)
         assert self.offset6.rollback(d) == d
         assert self.offset7.rollback(d) == d
+        assert self.offset8.rollback(d) == datetime(2014, 6, 30, 17)
+        assert self.offset9.rollback(d) == d
+        assert self.offset10.rollback(d) == d
 
         assert self._offset(5).rollback(self.d) == self.d
 
@@ -857,6 +954,9 @@ def testRollforward1(self):
                 datetime(2014, 7, 1, 20, 0))
         assert (self.offset7.rollforward(self.d) ==
                 datetime(2014, 7, 1, 21, 30))
+        assert self.offset8.rollforward(self.d) == self.d
+        assert self.offset9.rollforward(self.d) == self.d
+        assert self.offset10.rollforward(self.d) == datetime(2014, 7, 1, 13)
 
         d = datetime(2014, 7, 1, 0)
         assert self.offset1.rollforward(d) == datetime(2014, 7, 1, 9)
@@ -866,6 +966,9 @@ def testRollforward1(self):
         assert self.offset5.rollforward(d) == datetime(2014, 7, 1, 11)
         assert self.offset6.rollforward(d) == d
         assert self.offset7.rollforward(d) == d
+        assert self.offset8.rollforward(d) == datetime(2014, 7, 1, 9)
+        assert self.offset9.rollforward(d) == d
+        assert self.offset10.rollforward(d) == d
 
         assert self._offset(5).rollforward(self.d) == self.d
 
@@ -960,6 +1063,35 @@ def test_normalize(self, case):
         datetime(2014, 7, 6, 23, 0): False,
         datetime(2014, 7, 7, 3, 0): False}))
 
+    on_offset_cases.append((BusinessHour(start=['09:00', '13:00'],
+                                         end=['12:00', '17:00']), {
+        datetime(2014, 7, 1, 9): True,
+        datetime(2014, 7, 1, 8, 59): False,
+        datetime(2014, 7, 1, 8): False,
+        datetime(2014, 7, 1, 17): True,
+        datetime(2014, 7, 1, 17, 1): False,
+        datetime(2014, 7, 1, 18): False,
+        datetime(2014, 7, 5, 9): False,
+        datetime(2014, 7, 6, 12): False,
+        datetime(2014, 7, 1, 12, 30): False}))
+
+    on_offset_cases.append((BusinessHour(start=['19:00', '23:00'],
+                                         end=['21:00', '05:00']), {
+        datetime(2014, 7, 1, 9, 0): False,
+        datetime(2014, 7, 1, 10, 0): False,
+        datetime(2014, 7, 1, 15): False,
+        datetime(2014, 7, 1, 15, 1): False,
+        datetime(2014, 7, 5, 12, 0): False,
+        datetime(2014, 7, 6, 12, 0): False,
+        datetime(2014, 7, 1, 19, 0): True,
+        datetime(2014, 7, 2, 0, 0): True,
+        datetime(2014, 7, 4, 23): True,
+        datetime(2014, 7, 5, 1): True,
+        datetime(2014, 7, 5, 5, 0): True,
+        datetime(2014, 7, 6, 23, 0): False,
+        datetime(2014, 7, 7, 3, 0): False,
+        datetime(2014, 7, 4, 22): False}))
+
     @pytest.mark.parametrize('case', on_offset_cases)
     def test_onOffset(self, case):
         offset, cases = case
@@ -1125,6 +1257,76 @@ def test_onOffset(self, case):
         datetime(2014, 7, 7, 18): (datetime(2014, 7, 7, 17),
                                    datetime(2014, 7, 8, 17))}))
 
+    opening_time_cases.append(([BusinessHour(start=['11:15', '15:00'],
+                                             end=['13:00', '20:00']),
+                                BusinessHour(n=3, start=['11:15', '15:00'],
+                                             end=['12:00', '20:00']),
+                                BusinessHour(start=['11:15', '15:00'],
+                                             end=['13:00', '17:00']),
+                                BusinessHour(n=2, start=['11:15', '15:00'],
+                                             end=['12:00', '03:00']),
+                                BusinessHour(n=3, start=['11:15', '15:00'],
+                                             end=['13:00', '16:00'])], {
+        datetime(2014, 7, 1, 11): (datetime(2014, 7, 1, 11, 15),
+                                   datetime(2014, 6, 30, 15)),
+        datetime(2014, 7, 1, 18): (datetime(2014, 7, 2, 11, 15),
+                                   datetime(2014, 7, 1, 15)),
+        datetime(2014, 7, 1, 23): (datetime(2014, 7, 2, 11, 15),
+                                   datetime(2014, 7, 1, 15)),
+        datetime(2014, 7, 2, 8): (datetime(2014, 7, 2, 11, 15),
+                                  datetime(2014, 7, 1, 15)),
+        datetime(2014, 7, 2, 9): (datetime(2014, 7, 2, 11, 15),
+                                  datetime(2014, 7, 1, 15)),
+        datetime(2014, 7, 2, 10): (datetime(2014, 7, 2, 11, 15),
+                                   datetime(2014, 7, 1, 15)),
+        datetime(2014, 7, 2, 11, 15): (datetime(2014, 7, 2, 11, 15),
+                                       datetime(2014, 7, 2, 11, 15)),
+        datetime(2014, 7, 2, 11, 15, 1): (datetime(2014, 7, 2, 15),
+                                          datetime(2014, 7, 2, 11, 15)),
+        datetime(2014, 7, 5, 10): (datetime(2014, 7, 7, 11, 15),
+                                   datetime(2014, 7, 4, 15)),
+        datetime(2014, 7, 4, 10): (datetime(2014, 7, 4, 11, 15),
+                                   datetime(2014, 7, 3, 15)),
+        datetime(2014, 7, 4, 23): (datetime(2014, 7, 7, 11, 15),
+                                   datetime(2014, 7, 4, 15)),
+        datetime(2014, 7, 6, 10): (datetime(2014, 7, 7, 11, 15),
+                                   datetime(2014, 7, 4, 15)),
+        datetime(2014, 7, 7, 5): (datetime(2014, 7, 7, 11, 15),
+                                  datetime(2014, 7, 4, 15)),
+        datetime(2014, 7, 7, 9, 1): (datetime(2014, 7, 7, 11, 15),
+                                     datetime(2014, 7, 4, 15)),
+        datetime(2014, 7, 7, 12): (datetime(2014, 7, 7, 15),
+                                   datetime(2014, 7, 7, 11, 15))}))
+
+    opening_time_cases.append(([BusinessHour(n=-1, start=['17:00', '08:00'],
+                                             end=['05:00', '10:00']),
+                                BusinessHour(n=-2, start=['08:00', '17:00'],
+                                             end=['10:00', '03:00'])], {
+        datetime(2014, 7, 1, 11): (datetime(2014, 7, 1, 8),
+                                   datetime(2014, 7, 1, 17)),
+        datetime(2014, 7, 1, 18): (datetime(2014, 7, 1, 17),
+                                   datetime(2014, 7, 2, 8)),
+        datetime(2014, 7, 1, 23): (datetime(2014, 7, 1, 17),
+                                   datetime(2014, 7, 2, 8)),
+        datetime(2014, 7, 2, 8): (datetime(2014, 7, 2, 8),
+                                  datetime(2014, 7, 2, 8)),
+        datetime(2014, 7, 2, 9): (datetime(2014, 7, 2, 8),
+                                  datetime(2014, 7, 2, 17)),
+        datetime(2014, 7, 2, 16, 59): (datetime(2014, 7, 2, 8),
+                                       datetime(2014, 7, 2, 17)),
+        datetime(2014, 7, 5, 10): (datetime(2014, 7, 4, 17),
+                                   datetime(2014, 7, 7, 8)),
+        datetime(2014, 7, 4, 10): (datetime(2014, 7, 4, 8),
+                                   datetime(2014, 7, 4, 17)),
+        datetime(2014, 7, 4, 23): (datetime(2014, 7, 4, 17),
+                                   datetime(2014, 7, 7, 8)),
+        datetime(2014, 7, 6, 10): (datetime(2014, 7, 4, 17),
+                                   datetime(2014, 7, 7, 8)),
+        datetime(2014, 7, 7, 5): (datetime(2014, 7, 4, 17),
+                                  datetime(2014, 7, 7, 8)),
+        datetime(2014, 7, 7, 18): (datetime(2014, 7, 7, 17),
+                                   datetime(2014, 7, 8, 8))}))
+
     @pytest.mark.parametrize('case', opening_time_cases)
     def test_opening_time(self, case):
         _offsets, cases = case
@@ -1303,6 +1505,81 @@ def test_opening_time(self, case):
         datetime(2014, 7, 7, 3, 30, 30): datetime(2014, 7, 4, 22, 30, 30),
         datetime(2014, 7, 7, 3, 30, 20): datetime(2014, 7, 4, 22, 30, 20)}))
 
+    # multiple business hours
+    apply_cases.append((BusinessHour(start=['09:00', '14:00'],
+                                     end=['12:00', '18:00']), {
+        datetime(2014, 7, 1, 11): datetime(2014, 7, 1, 14),
+        datetime(2014, 7, 1, 15): datetime(2014, 7, 1, 16),
+        datetime(2014, 7, 1, 19): datetime(2014, 7, 2, 10),
+        datetime(2014, 7, 1, 16): datetime(2014, 7, 1, 17),
+        datetime(2014, 7, 1, 16, 30, 15): datetime(2014, 7, 1, 17, 30, 15),
+        datetime(2014, 7, 1, 17): datetime(2014, 7, 2, 9),
+        datetime(2014, 7, 2, 11): datetime(2014, 7, 2, 14),
+        # out of business hours
+        datetime(2014, 7, 1, 13): datetime(2014, 7, 1, 15),
+        datetime(2014, 7, 2, 8): datetime(2014, 7, 2, 10),
+        datetime(2014, 7, 2, 19): datetime(2014, 7, 3, 10),
+        datetime(2014, 7, 2, 23): datetime(2014, 7, 3, 10),
+        datetime(2014, 7, 3, 0): datetime(2014, 7, 3, 10),
+        # saturday
+        datetime(2014, 7, 5, 15): datetime(2014, 7, 7, 10),
+        datetime(2014, 7, 4, 17): datetime(2014, 7, 7, 9),
+        datetime(2014, 7, 4, 17, 30): datetime(2014, 7, 7, 9, 30),
+        datetime(2014, 7, 4, 17, 30, 30): datetime(2014, 7, 7, 9, 30, 30)}))
+
+    apply_cases.append((BusinessHour(n=4, start=['09:00', '14:00'],
+                                     end=['12:00', '18:00']), {
+        datetime(2014, 7, 1, 11): datetime(2014, 7, 1, 17),
+        datetime(2014, 7, 1, 13): datetime(2014, 7, 2, 9),
+        datetime(2014, 7, 1, 15): datetime(2014, 7, 2, 10),
+        datetime(2014, 7, 1, 16): datetime(2014, 7, 2, 11),
+        datetime(2014, 7, 1, 17): datetime(2014, 7, 2, 14),
+        datetime(2014, 7, 2, 11): datetime(2014, 7, 2, 17),
+        datetime(2014, 7, 2, 8): datetime(2014, 7, 2, 15),
+        datetime(2014, 7, 2, 19): datetime(2014, 7, 3, 15),
+        datetime(2014, 7, 2, 23): datetime(2014, 7, 3, 15),
+        datetime(2014, 7, 3, 0): datetime(2014, 7, 3, 15),
+        datetime(2014, 7, 5, 15): datetime(2014, 7, 7, 15),
+        datetime(2014, 7, 4, 17): datetime(2014, 7, 7, 14),
+        datetime(2014, 7, 4, 16, 30): datetime(2014, 7, 7, 11, 30),
+        datetime(2014, 7, 4, 16, 30, 30): datetime(2014, 7, 7, 11, 30, 30)}))
+
+    apply_cases.append((BusinessHour(n=-4, start=['09:00', '14:00'],
+                                     end=['12:00', '18:00']), {
+        datetime(2014, 7, 1, 11): datetime(2014, 6, 30, 16),
+        datetime(2014, 7, 1, 13): datetime(2014, 6, 30, 17),
+        datetime(2014, 7, 1, 15): datetime(2014, 6, 30, 18),
+        datetime(2014, 7, 1, 16): datetime(2014, 7, 1, 10),
+        datetime(2014, 7, 1, 17): datetime(2014, 7, 1, 11),
+        datetime(2014, 7, 2, 11): datetime(2014, 7, 1, 16),
+        datetime(2014, 7, 2, 8): datetime(2014, 7, 1, 12),
+        datetime(2014, 7, 2, 19): datetime(2014, 7, 2, 12),
+        datetime(2014, 7, 2, 23): datetime(2014, 7, 2, 12),
+        datetime(2014, 7, 3, 0): datetime(2014, 7, 2, 12),
+        datetime(2014, 7, 5, 15): datetime(2014, 7, 4, 12),
+        datetime(2014, 7, 4, 18): datetime(2014, 7, 4, 12),
+        datetime(2014, 7, 7, 9, 30): datetime(2014, 7, 4, 14, 30),
+        datetime(2014, 7, 7, 9, 30, 30): datetime(2014, 7, 4, 14, 30, 30)}))
+
+    apply_cases.append((BusinessHour(n=-1, start=['19:00', '03:00'],
+                                     end=['01:00', '05:00']), {
+        datetime(2014, 7, 1, 17): datetime(2014, 7, 1, 4),
+        datetime(2014, 7, 2, 14): datetime(2014, 7, 2, 4),
+        datetime(2014, 7, 2, 8): datetime(2014, 7, 2, 4),
+        datetime(2014, 7, 2, 13): datetime(2014, 7, 2, 4),
+        datetime(2014, 7, 2, 20): datetime(2014, 7, 2, 5),
+        datetime(2014, 7, 2, 19): datetime(2014, 7, 2, 4),
+        datetime(2014, 7, 2, 4): datetime(2014, 7, 2, 1),
+        datetime(2014, 7, 2, 19, 30): datetime(2014, 7, 2, 4, 30),
+        datetime(2014, 7, 3, 0): datetime(2014, 7, 2, 23),
+        datetime(2014, 7, 3, 6): datetime(2014, 7, 3, 4),
+        datetime(2014, 7, 4, 23): datetime(2014, 7, 4, 22),
+        datetime(2014, 7, 5, 0): datetime(2014, 7, 4, 23),
+        datetime(2014, 7, 5, 4): datetime(2014, 7, 5, 0),
+        datetime(2014, 7, 7, 3, 30): datetime(2014, 7, 5, 0, 30),
+        datetime(2014, 7, 7, 19, 30): datetime(2014, 7, 7, 4, 30),
+        datetime(2014, 7, 7, 19, 30, 30): datetime(2014, 7, 7, 4, 30, 30)}))
+
     @pytest.mark.parametrize('case', apply_cases)
     def test_apply(self, case):
         offset, cases = case
@@ -1359,6 +1636,42 @@ def test_apply(self, case):
         datetime(2014, 7, 7, 1): datetime(2014, 7, 15, 0),
         datetime(2014, 7, 7, 23, 30): datetime(2014, 7, 15, 21, 30)}))
 
+    # large n for multiple opening hours (3 days and 1 hour before)
+    apply_large_n_cases.append((BusinessHour(n=-25, start=['09:00', '14:00'],
+                                             end=['12:00', '19:00']), {
+        datetime(2014, 7, 1, 11): datetime(2014, 6, 26, 10),
+        datetime(2014, 7, 1, 13): datetime(2014, 6, 26, 11),
+        datetime(2014, 7, 1, 9): datetime(2014, 6, 25, 18),
+        datetime(2014, 7, 1, 10): datetime(2014, 6, 25, 19),
+        datetime(2014, 7, 3, 11): datetime(2014, 6, 30, 10),
+        datetime(2014, 7, 3, 8): datetime(2014, 6, 27, 18),
+        datetime(2014, 7, 3, 19): datetime(2014, 6, 30, 18),
+        datetime(2014, 7, 3, 23): datetime(2014, 6, 30, 18),
+        datetime(2014, 7, 4, 9): datetime(2014, 6, 30, 18),
+        datetime(2014, 7, 5, 15): datetime(2014, 7, 1, 18),
+        datetime(2014, 7, 6, 18): datetime(2014, 7, 1, 18),
+        datetime(2014, 7, 7, 9, 30): datetime(2014, 7, 1, 18, 30),
+        datetime(2014, 7, 7, 10, 30, 30): datetime(2014, 7, 2, 9, 30, 30)}))
+
+    # 5 days and 3 hours later
+    apply_large_n_cases.append((BusinessHour(28, start=['21:00', '03:00'],
+                                             end=['01:00', '04:00']), {
+        datetime(2014, 7, 1, 11): datetime(2014, 7, 9, 0),
+        datetime(2014, 7, 1, 22): datetime(2014, 7, 9, 3),
+        datetime(2014, 7, 1, 23): datetime(2014, 7, 9, 21),
+        datetime(2014, 7, 2, 2): datetime(2014, 7, 9, 23),
+        datetime(2014, 7, 3, 21): datetime(2014, 7, 11, 0),
+        datetime(2014, 7, 4, 1): datetime(2014, 7, 11, 23),
+        datetime(2014, 7, 4, 2): datetime(2014, 7, 11, 23),
+        datetime(2014, 7, 4, 3): datetime(2014, 7, 11, 23),
+        datetime(2014, 7, 4, 21): datetime(2014, 7, 12, 0),
+        datetime(2014, 7, 5, 0): datetime(2014, 7, 14, 22),
+        datetime(2014, 7, 5, 1): datetime(2014, 7, 14, 23),
+        datetime(2014, 7, 5, 15): datetime(2014, 7, 14, 23),
+        datetime(2014, 7, 6, 18): datetime(2014, 7, 14, 23),
+        datetime(2014, 7, 7, 1): datetime(2014, 7, 14, 23),
+        datetime(2014, 7, 7, 23, 30): datetime(2014, 7, 15, 21, 30)}))
+
     @pytest.mark.parametrize('case', apply_large_n_cases)
     def test_apply_large_n(self, case):
         offset, cases = case
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index ac20ad1669638..087c05574090c 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -17,6 +17,7 @@
 from pandas.util._decorators import Appender, Substitution, cache_readonly
 
 from pandas.core.dtypes.generic import ABCPeriod
+from pandas.core.dtypes.inference import is_list_like
 
 from pandas.core.tools.datetimes import to_datetime
 
@@ -581,9 +582,44 @@ class BusinessHourMixin(BusinessMixin):
 
     def __init__(self, start='09:00', end='17:00', offset=timedelta(0)):
         # must be validated here to equality check
-        start = liboffsets._validate_business_time(start)
+        if not is_list_like(start):
+            start = [start]
+        if not len(start):
+            raise ValueError('Must include at least 1 start time')
+
+        if not is_list_like(end):
+            end = [end]
+        if not len(end):
+            raise ValueError('Must include at least 1 end time')
+
+        start = np.array([liboffsets._validate_business_time(x)
+                          for x in start])
+        end = np.array([liboffsets._validate_business_time(x) for x in end])
+
+        # Validation of input
+        if len(start) != len(end):
+            raise ValueError('number of starting time and ending time '
+                             'must be the same')
+        num_openings = len(start)
+
+        # sort starting and ending time by starting time
+        index = np.argsort(start)
+
+        # convert to tuple so that start and end are hashable
+        start = tuple(start[index])
+        end = tuple(end[index])
+
+        total_secs = 0
+        for i in range(num_openings):
+            total_secs += self._get_business_hours_by_sec(start[i], end[i])
+            total_secs += self._get_business_hours_by_sec(
+                end[i], start[(i + 1) % num_openings])
+        if total_secs != 24 * 60 * 60:
+            raise ValueError('invalid starting and ending time(s): '
+                             'opening hours should not touch or overlap with '
+                             'one another')
+
         object.__setattr__(self, "start", start)
-        end = liboffsets._validate_business_time(end)
         object.__setattr__(self, "end", end)
         object.__setattr__(self, "_offset", offset)
 
@@ -605,62 +641,93 @@ def next_bday(self):
         else:
             return BusinessDay(n=nb_offset)
 
-    @cache_readonly
-    def _get_daytime_flag(self):
-        if self.start == self.end:
-            raise ValueError('start and end must not be the same')
-        elif self.start < self.end:
-            return True
-        else:
-            return False
-
-    def _next_opening_time(self, other):
+    def _next_opening_time(self, other, sign=1):
         """
-        If n is positive, return tomorrow's business day opening time.
-        Otherwise yesterday's business day's opening time.
+        If self.n and sign have the same sign, return the earliest opening time
+        later than or equal to current time.
+        Otherwise the latest opening time earlier than or equal to current
+        time.
 
         Opening time always locates on BusinessDay.
-        Otherwise, closing time may not if business hour extends over midnight.
+        However, closing time may not if business hour extends over midnight.
+
+        Parameters
+        ----------
+        other : datetime
+            Current time.
+        sign : int, default 1.
+            Either 1 or -1. Going forward in time if it has the same sign as
+            self.n. Going backward in time otherwise.
+
+        Returns
+        -------
+        result : datetime
+            Next opening time.
         """
+        earliest_start = self.start[0]
+        latest_start = self.start[-1]
+
         if not self.next_bday.onOffset(other):
-            other = other + self.next_bday
+            # today is not business day
+            other = other + sign * self.next_bday
+            if self.n * sign >= 0:
+                hour, minute = earliest_start.hour, earliest_start.minute
+            else:
+                hour, minute = latest_start.hour, latest_start.minute
         else:
-            if self.n >= 0 and self.start < other.time():
-                other = other + self.next_bday
-            elif self.n < 0 and other.time() < self.start:
-                other = other + self.next_bday
-        return datetime(other.year, other.month, other.day,
-                        self.start.hour, self.start.minute)
+            if self.n * sign >= 0:
+                if latest_start < other.time():
+                    # current time is after latest starting time in today
+                    other = other + sign * self.next_bday
+                    hour, minute = earliest_start.hour, earliest_start.minute
+                else:
+                    # find earliest starting time no earlier than current time
+                    for st in self.start:
+                        if other.time() <= st:
+                            hour, minute = st.hour, st.minute
+                            break
+            else:
+                if other.time() < earliest_start:
+                    # current time is before earliest starting time in today
+                    other = other + sign * self.next_bday
+                    hour, minute = latest_start.hour, latest_start.minute
+                else:
+                    # find latest starting time no later than current time
+                    for st in reversed(self.start):
+                        if other.time() >= st:
+                            hour, minute = st.hour, st.minute
+                            break
+
+        return datetime(other.year, other.month, other.day, hour, minute)
 
     def _prev_opening_time(self, other):
         """
-        If n is positive, return yesterday's business day opening time.
-        Otherwise yesterday business day's opening time.
+        If n is positive, return the latest opening time earlier than or equal
+        to current time.
+        Otherwise the earliest opening time later than or equal to current
+        time.
+
+        Parameters
+        ----------
+        other : datetime
+            Current time.
+
+        Returns
+        -------
+        result : datetime
+            Previous opening time.
         """
-        if not self.next_bday.onOffset(other):
-            other = other - self.next_bday
-        else:
-            if self.n >= 0 and other.time() < self.start:
-                other = other - self.next_bday
-            elif self.n < 0 and other.time() > self.start:
-                other = other - self.next_bday
-        return datetime(other.year, other.month, other.day,
-                        self.start.hour, self.start.minute)
+        return self._next_opening_time(other, sign=-1)
 
-    @cache_readonly
-    def _get_business_hours_by_sec(self):
+    def _get_business_hours_by_sec(self, start, end):
         """
         Return business hours in a day by seconds.
         """
-        if self._get_daytime_flag:
-            # create dummy datetime to calculate businesshours in a day
-            dtstart = datetime(2014, 4, 1, self.start.hour, self.start.minute)
-            until = datetime(2014, 4, 1, self.end.hour, self.end.minute)
-            return (until - dtstart).total_seconds()
-        else:
-            dtstart = datetime(2014, 4, 1, self.start.hour, self.start.minute)
-            until = datetime(2014, 4, 2, self.end.hour, self.end.minute)
-            return (until - dtstart).total_seconds()
+        # create dummy datetime to calculate businesshours in a day
+        dtstart = datetime(2014, 4, 1, start.hour, start.minute)
+        day = 1 if start < end else 2
+        until = datetime(2014, 4, day, end.hour, end.minute)
+        return int((until - dtstart).total_seconds())
 
     @apply_wraps
     def rollback(self, dt):
@@ -668,13 +735,11 @@ def rollback(self, dt):
         Roll provided date backward to next offset only if not on offset.
         """
         if not self.onOffset(dt):
-            businesshours = self._get_business_hours_by_sec
             if self.n >= 0:
-                dt = self._prev_opening_time(
-                    dt) + timedelta(seconds=businesshours)
+                dt = self._prev_opening_time(dt)
             else:
-                dt = self._next_opening_time(
-                    dt) + timedelta(seconds=businesshours)
+                dt = self._next_opening_time(dt)
+            return self._get_closing_time(dt)
         return dt
 
     @apply_wraps
@@ -689,11 +754,28 @@ def rollforward(self, dt):
                 return self._prev_opening_time(dt)
         return dt
 
+    def _get_closing_time(self, dt):
+        """
+        Get the closing time of a business hour interval by its opening time.
+
+        Parameters
+        ----------
+        dt : datetime
+            Opening time of a business hour interval.
+
+        Returns
+        -------
+        result : datetime
+            Corresponding closing time.
+        """
+        for i, st in enumerate(self.start):
+            if st.hour == dt.hour and st.minute == dt.minute:
+                return dt + timedelta(
+                    seconds=self._get_business_hours_by_sec(st, self.end[i]))
+        assert False
+
     @apply_wraps
     def apply(self, other):
-        businesshours = self._get_business_hours_by_sec
-        bhdelta = timedelta(seconds=businesshours)
-
         if isinstance(other, datetime):
             # used for detecting edge condition
             nanosecond = getattr(other, 'nanosecond', 0)
@@ -703,63 +785,75 @@ def apply(self, other):
                              other.hour, other.minute,
                              other.second, other.microsecond)
             n = self.n
+
+            # adjust other to reduce number of cases to handle
             if n >= 0:
-                if (other.time() == self.end or
-                        not self._onOffset(other, businesshours)):
+                if (other.time() in self.end or
+                        not self._onOffset(other)):
                     other = self._next_opening_time(other)
             else:
-                if other.time() == self.start:
+                if other.time() in self.start:
                     # adjustment to move to previous business day
                     other = other - timedelta(seconds=1)
-                if not self._onOffset(other, businesshours):
+                if not self._onOffset(other):
                     other = self._next_opening_time(other)
-                    other = other + bhdelta
+                    other = self._get_closing_time(other)
+
+            # get total business hours by sec in one business day
+            businesshours = sum(self._get_business_hours_by_sec(st, en)
+                                for st, en in zip(self.start, self.end))
 
             bd, r = divmod(abs(n * 60), businesshours // 60)
             if n < 0:
                 bd, r = -bd, -r
 
+            # adjust by business days first
             if bd != 0:
                 skip_bd = BusinessDay(n=bd)
                 # midnight business hour may not on BusinessDay
                 if not self.next_bday.onOffset(other):
-                    remain = other - self._prev_opening_time(other)
-                    other = self._next_opening_time(other + skip_bd) + remain
+                    prev_open = self._prev_opening_time(other)
+                    remain = other - prev_open
+                    other = prev_open + skip_bd + remain
                 else:
                     other = other + skip_bd
 
-            hours, minutes = divmod(r, 60)
-            result = other + timedelta(hours=hours, minutes=minutes)
-
-            # because of previous adjustment, time will be larger than start
-            if n >= 0:
-                bday_edge = self._prev_opening_time(other) + bhdelta
-                if bday_edge < result:
-                    bday_remain = result - bday_edge
-                    result = self._next_opening_time(other)
-                    result += bday_remain
-            else:
-                bday_edge = self._next_opening_time(other)
-                if bday_edge > result:
-                    bday_remain = result - bday_edge
-                    result = self._next_opening_time(result) + bhdelta
-                    result += bday_remain
+            # remaining business hours to adjust
+            bhour_remain = timedelta(minutes=r)
 
-            # edge handling
             if n >= 0:
-                if result.time() == self.end:
-                    result = self._next_opening_time(result)
+                while bhour_remain != timedelta(0):
+                    # business hour left in this business time interval
+                    bhour = self._get_closing_time(
+                        self._prev_opening_time(other)) - other
+                    if bhour_remain < bhour:
+                        # finish adjusting if possible
+                        other += bhour_remain
+                        bhour_remain = timedelta(0)
+                    else:
+                        # go to next business time interval
+                        bhour_remain -= bhour
+                        other = self._next_opening_time(other + bhour)
             else:
-                if result.time() == self.start and nanosecond == 0:
-                    # adjustment to move to previous business day
-                    result = self._next_opening_time(
-                        result - timedelta(seconds=1)) + bhdelta
+                while bhour_remain != timedelta(0):
+                    # business hour left in this business time interval
+                    bhour = self._next_opening_time(other) - other
+                    if (bhour_remain > bhour or
+                            bhour_remain == bhour and nanosecond != 0):
+                        # finish adjusting if possible
+                        other += bhour_remain
+                        bhour_remain = timedelta(0)
+                    else:
+                        # go to next business time interval
+                        bhour_remain -= bhour
+                        other = self._get_closing_time(
+                            self._next_opening_time(
+                                other + bhour - timedelta(seconds=1)))
 
-            return result
+            return other
         else:
-            # TODO: Figure out the end of this sente
             raise ApplyTypeError(
-                'Only know how to combine business hour with ')
+                'Only know how to combine business hour with datetime')
 
     def onOffset(self, dt):
         if self.normalize and not _is_normalized(dt):
@@ -770,10 +864,9 @@ def onOffset(self, dt):
                           dt.minute, dt.second, dt.microsecond)
         # Valid BH can be on the different BusinessDay during midnight
         # Distinguish by the time spent from previous opening time
-        businesshours = self._get_business_hours_by_sec
-        return self._onOffset(dt, businesshours)
+        return self._onOffset(dt)
 
-    def _onOffset(self, dt, businesshours):
+    def _onOffset(self, dt):
         """
         Slight speedups using calculated values.
         """
@@ -786,6 +879,11 @@ def _onOffset(self, dt, businesshours):
         else:
             op = self._next_opening_time(dt)
         span = (dt - op).total_seconds()
+        businesshours = 0
+        for i, st in enumerate(self.start):
+            if op.hour == st.hour and op.minute == st.minute:
+                businesshours = self._get_business_hours_by_sec(
+                    st, self.end[i])
         if span <= businesshours:
             return True
         else:
@@ -793,17 +891,17 @@ def _onOffset(self, dt, businesshours):
 
     def _repr_attrs(self):
         out = super()._repr_attrs()
-        start = self.start.strftime('%H:%M')
-        end = self.end.strftime('%H:%M')
-        attrs = ['{prefix}={start}-{end}'.format(prefix=self._prefix,
-                                                 start=start, end=end)]
+        hours = ','.join('{}-{}'.format(
+            st.strftime('%H:%M'), en.strftime('%H:%M'))
+            for st, en in zip(self.start, self.end))
+        attrs = ['{prefix}={hours}'.format(prefix=self._prefix, hours=hours)]
         out += ': ' + ', '.join(attrs)
         return out
 
 
 class BusinessHour(BusinessHourMixin, SingleConstructorOffset):
     """
-    DateOffset subclass representing possibly n business days.
+    DateOffset subclass representing possibly n business hours.
 
     .. versionadded:: 0.16.1
     """