diff --git a/pandas/core/reshape/reshape.py b/pandas/core/reshape/reshape.py
index 3d9e84954a63b..b22d143544b7b 100644
--- a/pandas/core/reshape/reshape.py
+++ b/pandas/core/reshape/reshape.py
@@ -395,15 +395,29 @@ def pivot(self, index=None, columns=None, values=None):
     See DataFrame.pivot
     """
     if values is None:
-        cols = [columns] if index is None else [index, columns]
+        if index is None:
+            cols = [columns]
+        else:
+            if is_list_like(index):
+                cols = [column for column in index]
+            else:
+                cols = [index]
+            cols.append(columns)
         append = index is None
         indexed = self.set_index(cols, append=append)
+
     else:
         if index is None:
             index = self.index
+            index = MultiIndex.from_arrays([index, self[columns]])
+        elif is_list_like(index):
+            # Iterating through the list of multiple columns of an index
+            indexes = [self[column] for column in index]
+            indexes.append(self[columns])
+            index = MultiIndex.from_arrays(indexes)
         else:
             index = self[index]
-        index = MultiIndex.from_arrays([index, self[columns]])
+            index = MultiIndex.from_arrays([index, self[columns]])
 
         if is_list_like(values) and not isinstance(values, tuple):
             # Exclude tuple because it is seen as a single column name
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index 7e7e081408534..4474c61dddfe3 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -301,6 +301,34 @@ def test_pivot_multi_functions(self):
         expected = concat([means, stds], keys=['mean', 'std'], axis=1)
         tm.assert_frame_equal(result, expected)
 
+    def test_pivot_multiple_columns_as_index(self):
+        # adding the test case for multiple columns as index (#21425)
+        df = DataFrame({'lev1': [1, 1, 1, 1, 2, 2, 2, 2],
+                        'lev2': [1, 1, 2, 2, 1, 1, 2, 2],
+                        'lev3': [1, 2, 1, 2, 1, 2, 1, 2],
+                        'values': [0, 1, 2, 3, 4, 5, 6, 7]})
+        result = df.pivot(index=['lev1', 'lev2'],
+                          columns='lev3',
+                          values='values')
+        result_no_values = df.pivot(index=['lev1', 'lev2'],
+                                    columns='lev3')
+        data = [[0, 1], [2, 3], [4, 5], [6, 7]]
+        exp_index = pd.MultiIndex.from_product([[1, 2], [1, 2]],
+                                               names=['lev1', 'lev2'])
+        exp_columns_1 = Index([1, 2], name='lev3')
+        expected_1 = DataFrame(data=data, index=exp_index,
+                               columns=exp_columns_1)
+
+        exp_columns_2 = MultiIndex(levels=[['values'], [1, 2]],
+                                   labels=[[0, 0], [0, 1]],
+                                   names=[None, 'lev3'])
+
+        expected_2 = DataFrame(data=data, index=exp_index,
+                               columns=exp_columns_2)
+
+        tm.assert_frame_equal(result, expected_1)
+        tm.assert_frame_equal(result_no_values, expected_2)
+
     def test_pivot_index_with_nan(self):
         # GH 3588
         nan = np.nan