diff --git a/colossalai/zero/low_level/low_level_optim.py b/colossalai/zero/low_level/low_level_optim.py
index a1e85e5b9..85ac9eb48 100644
--- a/colossalai/zero/low_level/low_level_optim.py
+++ b/colossalai/zero/low_level/low_level_optim.py
@@ -333,12 +333,23 @@ class LowLevelZeroOptimizer(OptimizerWrapper):
         self.zero_grad()
 
     def backward_by_grad(self, tensor, grad):
-        # in lower stage which grad is transfered by higher stage
-        # we need to pass the optim state down.
+        assert not(self._partition_grads and not self.require_grad_sync), \
+            "ZeRO2(partition_grads) and gradient accumulation(no_sync) are not compatible"
+
         if self.mixed_precision_mixin is not None:
             grad = self.mixed_precision_mixin.pre_backward_by_grad(tensor, grad)
         torch.autograd.backward(tensor, grad)
 
+        if not self.require_grad_sync:
+            return
+        self._reduce_grad(self._partition_grads)
+
+        # clear reduced grads
+        if self._overlap_communication:
+            torch.cuda.synchronize()
+
+        self.zero_grad()
+
     def zero_grad(self, set_to_none=True):
         """
         Set parameter gradients to zero. If set_to_none = True, gradient
diff --git a/tests/test_shardformer/test_model/test_shard_bert.py b/tests/test_shardformer/test_model/test_shard_bert.py
index 61881a1f9..0855e2248 100644
--- a/tests/test_shardformer/test_model/test_shard_bert.py
+++ b/tests/test_shardformer/test_model/test_shard_bert.py
@@ -163,6 +163,15 @@ def run_bert_test(test_config):
         'enable_all_optimization': False,
         'use_lazy_init': False,
         'precision': 'fp32',
+    },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
         'initial_scale': 1,
     },
 ])
diff --git a/tests/test_shardformer/test_model/test_shard_bloom.py b/tests/test_shardformer/test_model/test_shard_bloom.py
index f7ab94bc9..c9ee690c8 100644
--- a/tests/test_shardformer/test_model/test_shard_bloom.py
+++ b/tests/test_shardformer/test_model/test_shard_bloom.py
@@ -165,6 +165,16 @@ def run_bloom_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 def run_bloom_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_bloom')
diff --git a/tests/test_shardformer/test_model/test_shard_chatglm2.py b/tests/test_shardformer/test_model/test_shard_chatglm2.py
index c5a3e68f7..05ca05dea 100644
--- a/tests/test_shardformer/test_model/test_shard_chatglm2.py
+++ b/tests/test_shardformer/test_model/test_shard_chatglm2.py
@@ -165,6 +165,16 @@ def run_chatglm_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 def run_chatglm_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_chatglm')
diff --git a/tests/test_shardformer/test_model/test_shard_gpt2.py b/tests/test_shardformer/test_model/test_shard_gpt2.py
index 44914721c..563084ed0 100644
--- a/tests/test_shardformer/test_model/test_shard_gpt2.py
+++ b/tests/test_shardformer/test_model/test_shard_gpt2.py
@@ -183,6 +183,16 @@ def run_gpt2_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 @clear_cache_before_run()
 def run_gpt2_3d_test(test_config):
diff --git a/tests/test_shardformer/test_model/test_shard_llama.py b/tests/test_shardformer/test_model/test_shard_llama.py
index c9d5d3d08..a60150e3c 100644
--- a/tests/test_shardformer/test_model/test_shard_llama.py
+++ b/tests/test_shardformer/test_model/test_shard_llama.py
@@ -185,6 +185,16 @@ def run_llama_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 def run_llama_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_llama')
diff --git a/tests/test_shardformer/test_model/test_shard_opt.py b/tests/test_shardformer/test_model/test_shard_opt.py
index 8c0432b37..25b1eefc6 100644
--- a/tests/test_shardformer/test_model/test_shard_opt.py
+++ b/tests/test_shardformer/test_model/test_shard_opt.py
@@ -174,6 +174,16 @@ def run_opt_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 def run_opt_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_opt')
diff --git a/tests/test_shardformer/test_model/test_shard_t5.py b/tests/test_shardformer/test_model/test_shard_t5.py
index 29367031e..768cae0a6 100644
--- a/tests/test_shardformer/test_model/test_shard_t5.py
+++ b/tests/test_shardformer/test_model/test_shard_t5.py
@@ -170,6 +170,16 @@ def run_t5_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 4,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp16',
+        'zero_stage': 1,
+        'initial_scale': 1,
+    },
 ])
 def run_t5_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_t5')
diff --git a/tests/test_shardformer/test_model/test_shard_vit.py b/tests/test_shardformer/test_model/test_shard_vit.py
index 2980c6eea..15db63bfd 100644
--- a/tests/test_shardformer/test_model/test_shard_vit.py
+++ b/tests/test_shardformer/test_model/test_shard_vit.py
@@ -176,6 +176,15 @@ def run_vit_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 2,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp32',
+        'initial_scale': 1,
+    },
 ])
 def run_vit_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_vit')
diff --git a/tests/test_shardformer/test_model/test_shard_whisper.py b/tests/test_shardformer/test_model/test_shard_whisper.py
index a55753018..d0c04c98f 100644
--- a/tests/test_shardformer/test_model/test_shard_whisper.py
+++ b/tests/test_shardformer/test_model/test_shard_whisper.py
@@ -107,7 +107,7 @@ def check_forward_backward(model_fn, data_gen_fn, output_transform_fn, loss_fn,
 
     # check weights
     if test_config['precision'] == 'fp32':
-        atol, rtol = 5e-4, 5e-4
+        atol, rtol = 1e-3, 1e-3
     else:
         atol, rtol = 5e-3, 5e-3
     if stage_manager is None or stage_manager.is_first_stage():
@@ -195,6 +195,15 @@ def run_whisper_test(test_config):
         'precision': 'fp32',
         'initial_scale': 1,
     },
+    {
+        'tp_size': 2,
+        'pp_size': 2,
+        'num_microbatches': 2,
+        'enable_all_optimization': False,
+        'use_lazy_init': False,
+        'precision': 'fp32',
+        'initial_scale': 1,
+    },
 ])
 def run_whisper_3d_test(test_config):
     sub_model_zoo = model_zoo.get_sub_registry('transformers_whisper')