diff --git a/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass.cc b/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass.cc
index 62b2be712beef30bc0ae800fb6bb605ea89100eb..eebc87f5d99880a43394e41f1631fb9671efa9e1 100644
--- a/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass.cc
+++ b/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass.cc
@@ -186,9 +186,22 @@ class DeQuantizer final : public Quanter {
   // Checking whether a reorder from BF16 to FP32
   // should be added after the output to the operator
   bool IsNotPermittedName(const std::string& output_name) const override {
-    // XShape is output in transpose2 and reshape2 operators used to store the
-    // shape and lod of X. So this output do not need dequantize before.
-    return (output_name == "XShape");
+    std::unordered_map<std::string, std::vector<std::string>> block_list{
+        {"layer_norm",
+         {"Mean", "Variance"}}};  // not used in inference in MKLDNN
+
+    std::vector<std::string> blocked_outputs{"XShape"};  // blocklist for any op
+    auto op_name = op->Name();
+    if (block_list.count(op_name)) {
+      const auto& op_blocklist = block_list[op_name];
+      blocked_outputs.insert(blocked_outputs.begin(), op_blocklist.begin(),
+                             op_blocklist.end());
+    }
+
+    return std::any_of(blocked_outputs.begin(), blocked_outputs.end(),
+                       [&output_name](const std::string& name) {
+                         return name == output_name;
+                       });
   }
 
   std::string get_op_type() const override { return "dequantize"; };
diff --git a/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass_tester.cc b/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass_tester.cc
index 877ee71fc2d85dd6ac7bcf4c2e41cc92e3e2ef2d..3f5e9a1484841e090153c03751ed176a94034967 100644
--- a/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass_tester.cc
+++ b/paddle/fluid/framework/ir/mkldnn/cpu_bfloat16_pass_tester.cc
@@ -65,22 +65,20 @@ void SetOp(ProgramDesc* prog, const std::string& type, const std::string& name,
 static const std::initializer_list<std::string> variable_names{
     "z", "a", "b", "c", "d", "e", "f", "g", "h", "i"};
 
-void PreparePass(std::unique_ptr<ir::Graph>* graph, const ProgramDesc& prog,
-                 const std::initializer_list<std::string> variable_names,
-                 int* original_nodes_num, int* current_nodes_num) {
+void PreparePass(std::unique_ptr<ir::Graph>& graph, int* original_nodes_num,
+                 int* current_nodes_num) {
   auto pass = PassRegistry::Instance().Get("cpu_bfloat16_pass");
 
-  *original_nodes_num = (*graph)->Nodes().size();
-  (*graph).reset(pass->Apply((*graph).release()));
-  *current_nodes_num = (*graph)->Nodes().size();
+  *original_nodes_num = graph->Nodes().size();
+  graph.reset(pass->Apply(graph.release()));
+  *current_nodes_num = graph->Nodes().size();
 }
 
 void MainTest(const ProgramDesc& prog, const int& quant_count,
               const int& dequant_count, const int& added_nodes_count) {
-  std::unique_ptr<ir::Graph> graph(new ir::Graph(prog));
+  auto graph = std::make_unique<ir::Graph>(prog);
   int original_nodes_num, current_nodes_num;
-  PreparePass(&graph, prog, variable_names, &original_nodes_num,
-              &current_nodes_num);
+  PreparePass(graph, &original_nodes_num, &current_nodes_num);
 
   int quantize_nodes_count = 0;
   int dequantize_nodes_count = 0;