diff --git a/doc/source/whatsnew/v0.19.0.txt b/doc/source/whatsnew/v0.19.0.txt
index 657de7ec26efc..6a1d450cf083f 100644
--- a/doc/source/whatsnew/v0.19.0.txt
+++ b/doc/source/whatsnew/v0.19.0.txt
@@ -473,7 +473,7 @@ Bug Fixes
 - Bug in ``Series.str.extractall()`` with ``str`` index raises ``ValueError``  (:issue:`13156`)
 - Bug in ``Series.str.extractall()`` with single group and quantifier  (:issue:`13382`)
 
-
+- Bug in ``DatetimeIndex`` and ``Period`` subtraction raises ``ValueError`` or ``AttributeError`` rather than ``TypeError`` (:issue:`13078`)
 - Bug in ``PeriodIndex`` and ``Period`` subtraction raises ``AttributeError`` (:issue:`13071`)
 - Bug in ``PeriodIndex`` construction returning a ``float64`` index in some circumstances (:issue:`13067`)
 - Bug in ``.resample(..)`` with a ``PeriodIndex`` not changing its ``freq`` appropriately when empty (:issue:`13067`)
diff --git a/pandas/tseries/tests/test_base.py b/pandas/tseries/tests/test_base.py
index 7077a23d5abcb..4ed42d044c0a9 100644
--- a/pandas/tseries/tests/test_base.py
+++ b/pandas/tseries/tests/test_base.py
@@ -443,6 +443,20 @@ def test_sub_isub(self):
             rng -= 1
             tm.assert_index_equal(rng, expected)
 
+    def test_sub_period(self):
+        # GH 13078
+        # not supported, check TypeError
+        p = pd.Period('2011-01-01', freq='D')
+
+        for freq in [None, 'D']:
+            idx = pd.DatetimeIndex(['2011-01-01', '2011-01-02'], freq=freq)
+
+            with tm.assertRaises(TypeError):
+                idx - p
+
+            with tm.assertRaises(TypeError):
+                p - idx
+
     def test_value_counts_unique(self):
         # GH 7735
         for tz in [None, 'UTC', 'Asia/Tokyo', 'US/Eastern']:
@@ -1157,6 +1171,20 @@ def test_dti_tdi_numeric_ops(self):
         expected = DatetimeIndex(['20121231', pd.NaT, '20130101'])
         tm.assert_index_equal(result, expected)
 
+    def test_sub_period(self):
+        # GH 13078
+        # not supported, check TypeError
+        p = pd.Period('2011-01-01', freq='D')
+
+        for freq in [None, 'H']:
+            idx = pd.TimedeltaIndex(['1 hours', '2 hours'], freq=freq)
+
+            with tm.assertRaises(TypeError):
+                idx - p
+
+            with tm.assertRaises(TypeError):
+                p - idx
+
     def test_addition_ops(self):
 
         # with datetimes/timedelta and tdi/dti