diff --git a/pandas/tests/frame/test_sorting.py b/pandas/tests/frame/test_sorting.py
index 246ba943a4509..96aeb608ba3b8 100644
--- a/pandas/tests/frame/test_sorting.py
+++ b/pandas/tests/frame/test_sorting.py
@@ -227,6 +227,18 @@ def test_stable_descending_multicolumn_sort(self):
                                    kind='mergesort')
         assert_frame_equal(sorted_df, expected)
 
+    def test_sort_multi_index(self):
+        # GH 25775, testing that sorting by index works with a multi-index.
+        df = DataFrame({'a': [3, 1, 2], 'b': [0, 0, 0],
+                        'c': [0, 1, 2], 'd': list('abc')})
+        result = df.set_index(list('abc')).sort_index(level=list('ba'))
+
+        expected = DataFrame({'a': [1, 2, 3], 'b': [0, 0, 0],
+                              'c': [1, 2, 0], 'd': list('bca')})
+        expected = expected.set_index(list('abc'))
+
+        tm.assert_frame_equal(result, expected)
+
     def test_stable_categorial(self):
         # GH 16793
         df = DataFrame({