diff --git a/mmcv/cnn/bricks/conv_module.py b/mmcv/cnn/bricks/conv_module.py
index e71d243e15..4f19f1d0cf 100644
--- a/mmcv/cnn/bricks/conv_module.py
+++ b/mmcv/cnn/bricks/conv_module.py
@@ -3,6 +3,7 @@
 
 import torch.nn as nn
 
+from mmcv.utils import _BatchNorm, _InstanceNorm
 from ..utils import constant_init, kaiming_init
 from .activation import build_activation_layer
 from .conv import build_conv_layer
@@ -104,9 +105,6 @@ def __init__(self,
             bias = not self.with_norm
         self.with_bias = bias
 
-        if self.with_norm and self.with_bias:
-            warnings.warn('ConvModule has norm and bias at the same time')
-
         if self.with_explicit_padding:
             pad_cfg = dict(type=padding_mode)
             self.padding_layer = build_padding_layer(pad_cfg, padding)
@@ -147,6 +145,10 @@ def __init__(self,
                 norm_channels = in_channels
             self.norm_name, norm = build_norm_layer(norm_cfg, norm_channels)
             self.add_module(self.norm_name, norm)
+            if self.with_bias:
+                if isinstance(norm, (_BatchNorm, _InstanceNorm)):
+                    warnings.warn(
+                        'Unnecessary conv bias before batch/instance norm')
         else:
             self.norm_name = None
 
diff --git a/tests/test_cnn/test_conv_module.py b/tests/test_cnn/test_conv_module.py
index 63dc61ab87..e231ef3ae3 100644
--- a/tests/test_cnn/test_conv_module.py
+++ b/tests/test_cnn/test_conv_module.py
@@ -1,3 +1,4 @@
+import warnings
 from unittest.mock import patch
 
 import pytest
@@ -161,12 +162,27 @@ def test_bias():
     conv = ConvModule(3, 8, 2, bias=False)
     assert conv.conv.bias is None
 
-    # bias: True, with norm
+    # bias: True, with batch norm
     with pytest.warns(UserWarning) as record:
         ConvModule(3, 8, 2, bias=True, norm_cfg=dict(type='BN'))
     assert len(record) == 1
     assert record[0].message.args[
-        0] == 'ConvModule has norm and bias at the same time'
+        0] == 'Unnecessary conv bias before batch/instance norm'
+
+    # bias: True, with instance norm
+    with pytest.warns(UserWarning) as record:
+        ConvModule(3, 8, 2, bias=True, norm_cfg=dict(type='IN'))
+    assert len(record) == 1
+    assert record[0].message.args[
+        0] == 'Unnecessary conv bias before batch/instance norm'
+
+    # bias: True, with other norm
+    with pytest.warns(UserWarning) as record:
+        norm_cfg = dict(type='GN', num_groups=1)
+        ConvModule(3, 8, 2, bias=True, norm_cfg=norm_cfg)
+        warnings.warn('No warnings')
+    assert len(record) == 1
+    assert record[0].message.args[0] == 'No warnings'
 
 
 def conv_forward(self, x):