diff --git a/python/paddle/fluid/tests/unittests/test_dygraph_weight_norm.py b/python/paddle/fluid/tests/unittests/test_dygraph_weight_norm.py
index 466226c53fabb..a963c2ece0958 100644
--- a/python/paddle/fluid/tests/unittests/test_dygraph_weight_norm.py
+++ b/python/paddle/fluid/tests/unittests/test_dygraph_weight_norm.py
@@ -121,6 +121,9 @@ def test_check_output(self):
         before_weight = linear.weight.numpy()
         if self.dim == None:
             self.dim = -1
+
+        if self.dim != -1:
+            self.dim = (self.dim + len(before_weight)) % len(before_weight)
         wn = weight_norm(linear, dim=self.dim)
         outputs = []
         for name, data in self.data.items():
@@ -158,6 +161,13 @@ def init_test_case(self):
         self.dim = 3
 
 
+class TestDygraphWeightNormCase4(TestDygraphWeightNorm):
+    def init_test_case(self):
+        self.batch_size = 3
+        self.data_desc = (['x', [2, 3, 3]], )
+        self.dim = -3
+
+
 class TestDygraphRemoveWeightNorm(unittest.TestCase):
     def setUp(self):
         self.init_test_case()
diff --git a/python/paddle/fluid/tests/unittests/test_sync_batch_norm_op.py b/python/paddle/fluid/tests/unittests/test_sync_batch_norm_op.py
index 09cd40d9cc599..1c11e831b0ad3 100644
--- a/python/paddle/fluid/tests/unittests/test_sync_batch_norm_op.py
+++ b/python/paddle/fluid/tests/unittests/test_sync_batch_norm_op.py
@@ -227,14 +227,15 @@ def test_convert(self):
             return
 
         with program_guard(Program(), Program()):
+            compare_model = paddle.nn.Sequential(
+                paddle.nn.Conv2d(3, 5, 3), paddle.nn.BatchNorm2d(5))
             model = paddle.nn.Sequential(
                 paddle.nn.Conv2d(3, 5, 3), paddle.nn.BatchNorm2d(5))
-            sync_model = paddle.nn.SyncBatchNorm.convert_sync_batchnorm(model)
-            for idx, sublayer in enumerate(model.sublayers()):
+            model = paddle.nn.SyncBatchNorm.convert_sync_batchnorm(model)
+            for idx, sublayer in enumerate(compare_model.sublayers()):
                 if isinstance(sublayer, paddle.nn.BatchNorm2d):
                     self.assertEqual(
-                        isinstance(sync_model[idx], paddle.nn.SyncBatchNorm),
-                        True)
+                        isinstance(model[idx], paddle.nn.SyncBatchNorm), True)
 
 
 if __name__ == '__main__':
diff --git a/python/paddle/nn/layer/norm.py b/python/paddle/nn/layer/norm.py
index d13bf66ba5bfe..2000fbf388f88 100644
--- a/python/paddle/nn/layer/norm.py
+++ b/python/paddle/nn/layer/norm.py
@@ -1130,10 +1130,10 @@ def convert_sync_batchnorm(cls, layer):
         """
         layer_output = layer
         if isinstance(layer, _BatchNormBase):
-            layer_output = SyncBatchNorm(layer._num_features, layer._epsilon,
-                                         layer._momentum, layer._weight_attr,
-                                         layer._bias_attr, layer._data_format,
-                                         layer._name)
+            layer_output = SyncBatchNorm(
+                layer._num_features, layer._momentum, layer._epsilon,
+                layer._weight_attr, layer._bias_attr, layer._data_format,
+                layer._track_running_stats, layer._name)
 
             if layer._weight_attr != False and layer._bias_attr != False:
                 with no_grad():
diff --git a/python/paddle/nn/utils/weight_norm_hook.py b/python/paddle/nn/utils/weight_norm_hook.py
index ad53bf394660f..7a21e7661d4e7 100644
--- a/python/paddle/nn/utils/weight_norm_hook.py
+++ b/python/paddle/nn/utils/weight_norm_hook.py
@@ -112,6 +112,14 @@ def apply(layer, name, dim):
         if dim is None:
             dim = -1
 
+        # support dim is negative numeber, (dim = -1) == (dim = None)
+        weight_dim = len(layer._parameters[name].shape)
+        assert (
+            dim < weight_dim and dim >= -1 * weight_dim
+        ), "dim must set between [-R, R), R means the dimension of weight."
+        if dim != -1:
+            dim = (dim + weight_dim) % weight_dim
+
         fn = WeightNorm(name, dim)
 
         w = getattr(layer, name)