diff --git a/databricks/koalas/indexes.py b/databricks/koalas/indexes.py
index 7f78bb8a7d..b891c329ff 100644
--- a/databricks/koalas/indexes.py
+++ b/databricks/koalas/indexes.py
@@ -777,6 +777,78 @@ def symmetric_difference(self, other, result_name=None, sort=None):
 
         return result
 
+    # TODO: return_indexer
+    def sort_values(self, ascending=True):
+        """
+        Return a sorted copy of the index.
+
+        .. note:: This method is not supported for pandas when index has NaN value.
+                  pandas raises unexpected TypeError, but we support treating NaN
+                  as the smallest value.
+
+        Parameters
+        ----------
+        ascending : bool, default True
+            Should the index values be sorted in an ascending order.
+
+        Returns
+        -------
+        sorted_index : ks.Index or ks.MultiIndex
+            Sorted copy of the index.
+
+        See Also
+        --------
+        Series.sort_values : Sort values of a Series.
+        DataFrame.sort_values : Sort values in a DataFrame.
+
+        Examples
+        --------
+        >>> idx = ks.Index([10, 100, 1, 1000])
+        >>> idx
+        Int64Index([10, 100, 1, 1000], dtype='int64')
+
+        Sort values in ascending order (default behavior).
+
+        >>> idx.sort_values()
+        Int64Index([1, 10, 100, 1000], dtype='int64')
+
+        Sort values in descending order.
+
+        >>> idx.sort_values(ascending=False)
+        Int64Index([1000, 100, 10, 1], dtype='int64')
+
+        Support for MultiIndex.
+
+        >>> kidx = ks.MultiIndex.from_tuples([('a', 'x', 1), ('c', 'y', 2), ('b', 'z', 3)])
+        >>> kidx  # doctest: +SKIP
+        MultiIndex([('a', 'x', 1),
+                    ('c', 'y', 2),
+                    ('b', 'z', 3)],
+                   )
+
+        >>> kidx.sort_values()  # doctest: +SKIP
+        MultiIndex([('a', 'x', 1),
+                    ('b', 'z', 3),
+                    ('c', 'y', 2)],
+                   )
+
+        >>> kidx.sort_values(ascending=False)  # doctest: +SKIP
+        MultiIndex([('c', 'y', 2),
+                    ('b', 'z', 3),
+                    ('a', 'x', 1)],
+                   )
+        """
+        sdf = self._internal.sdf
+        sdf = sdf.orderBy(self._internal.index_scols, ascending=ascending)
+
+        internal = _InternalFrame(
+            sdf=sdf.select(self._internal.index_scols),
+            index_map=self._kdf._internal.index_map)
+
+        result = DataFrame(internal).index
+
+        return result
+
     def sort(self, *args, **kwargs):
         """
         Use sort_values instead.
diff --git a/databricks/koalas/missing/indexes.py b/databricks/koalas/missing/indexes.py
index d6bf755371..cce2a86636 100644
--- a/databricks/koalas/missing/indexes.py
+++ b/databricks/koalas/missing/indexes.py
@@ -81,7 +81,6 @@ class _MissingPandasLikeIndex(object):
     set_value = unsupported_function('set_value')
     slice_indexer = unsupported_function('slice_indexer')
     slice_locs = unsupported_function('slice_locs')
-    sort_values = unsupported_function('sort_values')
     sortlevel = unsupported_function('sortlevel')
     take = unsupported_function('take')
     to_flat_index = unsupported_function('to_flat_index')
@@ -173,7 +172,6 @@ class _MissingPandasLikeMultiIndex(object):
     set_value = unsupported_function('set_value')
     slice_indexer = unsupported_function('slice_indexer')
     slice_locs = unsupported_function('slice_locs')
-    sort_values = unsupported_function('sort_values')
     sortlevel = unsupported_function('sortlevel')
     swaplevel = unsupported_function('swaplevel')
     take = unsupported_function('take')
diff --git a/databricks/koalas/tests/test_indexes.py b/databricks/koalas/tests/test_indexes.py
index f858a7b8b9..7f8e01b29e 100644
--- a/databricks/koalas/tests/test_indexes.py
+++ b/databricks/koalas/tests/test_indexes.py
@@ -335,6 +335,28 @@ def test_index_fillna(self):
         with self.assertRaisesRegex(TypeError, "Unsupported type <class 'list'>"):
             kidx.fillna([1, 2])
 
+    def test_sort_values(self):
+        pidx = pd.Index([-10, -100, 200, 100])
+        kidx = ks.Index([-10, -100, 200, 100])
+
+        self.assert_eq(pidx.sort_values(), kidx.sort_values())
+        self.assert_eq(pidx.sort_values(ascending=False), kidx.sort_values(ascending=False))
+
+        pidx.name = 'koalas'
+        kidx.name = 'koalas'
+
+        self.assert_eq(pidx.sort_values(), kidx.sort_values())
+        self.assert_eq(pidx.sort_values(ascending=False), kidx.sort_values(ascending=False))
+
+        pidx = pd.MultiIndex.from_tuples([('a', 'x', 1), ('b', 'y', 2), ('c', 'z', 3)])
+        kidx = ks.MultiIndex.from_tuples([('a', 'x', 1), ('b', 'y', 2), ('c', 'z', 3)])
+
+        pidx.names = ['hello', 'koalas', 'goodbye']
+        kidx.names = ['hello', 'koalas', 'goodbye']
+
+        self.assert_eq(pidx.sort_values(), kidx.sort_values())
+        self.assert_eq(pidx.sort_values(ascending=False), kidx.sort_values(ascending=False))
+
     def test_index_drop_duplicates(self):
         pidx = pd.Index([1, 1, 2])
         kidx = ks.Index([1, 1, 2])
diff --git a/docs/source/reference/indexing.rst b/docs/source/reference/indexing.rst
index 5a00f8a65c..eaa9e57ad6 100644
--- a/docs/source/reference/indexing.rst
+++ b/docs/source/reference/indexing.rst
@@ -76,6 +76,13 @@ Conversion
    Index.to_series
    Index.to_numpy
 
+Sorting
+~~~~~~~
+.. autosummary::
+   :toctree: api/
+
+   Index.sort_values
+
 Time-specific operations
 ~~~~~~~~~~~~~~~~~~~~~~~~
 .. autosummary::
@@ -163,3 +170,10 @@ MultiIndex Conversion
 
    MultiIndex.astype
    MultiIndex.to_numpy
+
+MultiIndex Sorting
+~~~~~~~~~~~~~~~~~~
+.. autosummary::
+   :toctree: api/
+
+   MultiIndex.sort_values