diff --git a/asv_bench/benchmarks/index_object.py b/asv_bench/benchmarks/index_object.py
index 3fb53ce9b3c98..454d9ccdda102 100644
--- a/asv_bench/benchmarks/index_object.py
+++ b/asv_bench/benchmarks/index_object.py
@@ -199,3 +199,23 @@ def time_datetime_level_values_full(self):
 
     def time_datetime_level_values_sliced(self):
         self.mi[:10].values
+
+
+class Range(object):
+    goal_time = 0.2
+
+    def setup(self):
+        self.idx_inc = RangeIndex(start=0, stop=10**7, step=3)
+        self.idx_dec = RangeIndex(start=10**7, stop=-1, step=-3)
+
+    def time_max(self):
+        self.idx_inc.max()
+
+    def time_max_trivial(self):
+        self.idx_dec.max()
+
+    def time_min(self):
+        self.idx_dec.min()
+
+    def time_min_trivial(self):
+        self.idx_inc.min()
diff --git a/doc/source/api.rst b/doc/source/api.rst
index 6b3e6bedcb24b..96c7f68f57aaa 100644
--- a/doc/source/api.rst
+++ b/doc/source/api.rst
@@ -1416,6 +1416,20 @@ Selecting
    Index.slice_indexer
    Index.slice_locs
 
+.. _api.numericindex:
+
+Numeric Index
+-------------
+
+.. autosummary::
+   :toctree: generated/
+   :template: autosummary/class_without_autosummary.rst
+
+   RangeIndex
+   Int64Index
+   UInt64Index
+   Float64Index
+
 .. _api.categoricalindex:
 
 CategoricalIndex
diff --git a/doc/source/whatsnew/v0.21.0.txt b/doc/source/whatsnew/v0.21.0.txt
index 8bc9834ebef09..6157d73a76b31 100644
--- a/doc/source/whatsnew/v0.21.0.txt
+++ b/doc/source/whatsnew/v0.21.0.txt
@@ -473,6 +473,7 @@ Performance Improvements
 - Improved performance of :meth:`Categorical.set_categories` by not materializing the values (:issue:`17508`)
 - :attr:`Timestamp.microsecond` no longer re-computes on attribute access (:issue:`17331`)
 - Improved performance of the :class:`CategoricalIndex` for data that is already categorical dtype (:issue:`17513`)
+- Improved performance of :meth:`RangeIndex.min` and :meth:`RangeIndex.max` by using ``RangeIndex`` properties to perform the computations (:issue:`17607`)
 
 .. _whatsnew_0210.bug_fixes:
 
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index b759abaed4e56..16523257c2f77 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -269,6 +269,24 @@ def copy(self, name=None, deep=False, dtype=None, **kwargs):
         return RangeIndex(name=name, fastpath=True,
                           **dict(self._get_data_as_items()))
 
+    def _minmax(self, meth):
+        no_steps = len(self) - 1
+        if no_steps == -1:
+            return np.nan
+        elif ((meth == 'min' and self._step > 0) or
+              (meth == 'max' and self._step < 0)):
+            return self._start
+
+        return self._start + self._step * no_steps
+
+    def min(self):
+        """The minimum value of the RangeIndex"""
+        return self._minmax('min')
+
+    def max(self):
+        """The maximum value of the RangeIndex"""
+        return self._minmax('max')
+
     def argsort(self, *args, **kwargs):
         """
         Returns the indices that would sort the index and its
diff --git a/pandas/tests/indexes/test_range.py b/pandas/tests/indexes/test_range.py
index d206c36ee51c9..8dc5a40ced4bf 100644
--- a/pandas/tests/indexes/test_range.py
+++ b/pandas/tests/indexes/test_range.py
@@ -10,7 +10,7 @@
 
 import numpy as np
 
-from pandas import (notna, Series, Index, Float64Index,
+from pandas import (isna, notna, Series, Index, Float64Index,
                     Int64Index, RangeIndex)
 
 import pandas.util.testing as tm
@@ -994,3 +994,22 @@ def test_append(self):
                 # Append single item rather than list
                 result2 = indices[0].append(indices[1])
                 tm.assert_index_equal(result2, expected, exact=True)
+
+    @pytest.mark.parametrize('start,stop,step',
+                             [(0, 400, 3), (500, 0, -6), (-10**6, 10**6, 4),
+                              (10**6, -10**6, -4), (0, 10, 20)])
+    def test_max_min(self, start, stop, step):
+        # GH17607
+        idx = RangeIndex(start, stop, step)
+        expected = idx._int64index.max()
+        result = idx.max()
+        assert result == expected
+
+        expected = idx._int64index.min()
+        result = idx.min()
+        assert result == expected
+
+        # empty
+        idx = RangeIndex(start, stop, -step)
+        assert isna(idx.max())
+        assert isna(idx.min())