diff --git a/test/torchaudio_unittest/transforms/autograd_test_impl.py b/test/torchaudio_unittest/transforms/autograd_test_impl.py
index b8fe6c1863..717a7bc87b 100644
--- a/test/torchaudio_unittest/transforms/autograd_test_impl.py
+++ b/test/torchaudio_unittest/transforms/autograd_test_impl.py
@@ -154,6 +154,23 @@ def test_vol(self, gain, gain_type):
         waveform = get_whitenoise(sample_rate=sample_rate, duration=0.05, n_channels=2)
         self.assert_grad(transform, [waveform])
 
+    @parameterized.expand([
+        ({'cmn_window': 100, 'min_cmn_window': 50, 'center': False, 'norm_vars': False}, ),
+        ({'cmn_window': 100, 'min_cmn_window': 50, 'center': True, 'norm_vars': False}, ),
+        ({'cmn_window': 100, 'min_cmn_window': 50, 'center': False, 'norm_vars': True}, ),
+        ({'cmn_window': 100, 'min_cmn_window': 50, 'center': True, 'norm_vars': True}, ),
+    ])
+    def test_sliding_window_cmn(self, kwargs):
+        n_fft = 10
+        power = 1
+        spec = get_spectrogram(
+            get_whitenoise(sample_rate=200, duration=0.05, n_channels=2),
+            n_fft=n_fft, power=power)
+        spec_reshaped = spec.transpose(-1, -2)
+
+        transform = T.SlidingWindowCmn(**kwargs)
+        self.assert_grad(transform, [spec_reshaped])
+
     @unittest.expectedFailure
     def test_timestretch_zeros_fail(self):
         """Test that ``T.TimeStretch`` fails gradcheck at 0