diff --git a/python/paddle/fluid/tests/unittests/test_distribution.py b/python/paddle/fluid/tests/unittests/test_distribution.py
index 2946af2f4b72c5787a2da80eddae7bf8a96b45e0..bfc128e85e9caefd148fbbe25e378feaa39eb882 100644
--- a/python/paddle/fluid/tests/unittests/test_distribution.py
+++ b/python/paddle/fluid/tests/unittests/test_distribution.py
@@ -396,11 +396,18 @@ class NormalTest(unittest.TestCase):
         np_other_normal = NormalNumpy(self.other_loc_np, self.other_scale_np)
         np_kl = np_normal.kl_divergence(np_other_normal)
 
+        # Because assign op does not support the input of numpy.ndarray whose dtype is FP64.
+        # When loc and scale are FP64 numpy.ndarray, we need to use assign op to convert it
+        #  to FP32 Tensor. And then use cast op to convert it to a FP64 Tensor.
+        # There is a loss of accuracy in this conversion.
+        # So set the tolerance from 1e-6 to 1e-4.
+        log_tolerance = 1e-4
+
         np.testing.assert_equal(sample.shape, np_sample.shape)
         np.testing.assert_allclose(
             entropy, np_entropy, rtol=tolerance, atol=tolerance)
         np.testing.assert_allclose(
-            log_prob, np_lp, rtol=tolerance, atol=tolerance)
+            log_prob, np_lp, rtol=log_tolerance, atol=log_tolerance)
         np.testing.assert_allclose(probs, np_p, rtol=tolerance, atol=tolerance)
         np.testing.assert_allclose(kl, np_kl, rtol=tolerance, atol=tolerance)