diff --git a/paddle/fluid/framework/ir/auto_mixed_precision_pass.cc b/paddle/fluid/framework/ir/auto_mixed_precision_pass.cc
index bc034301989b0..44b41a89700de 100644
--- a/paddle/fluid/framework/ir/auto_mixed_precision_pass.cc
+++ b/paddle/fluid/framework/ir/auto_mixed_precision_pass.cc
@@ -437,6 +437,20 @@ void AutoMixedPrecisionPass::UpdateOpPrecision() const {
             vars_should_not_low_precision.insert(in_var_node->Var()->Name());
           }
         }
+
+        // when op_1 only support cpu kernel. if op_2's intput var is op_1's
+        // output var, then op_2 should not run half.
+        if (GetOpOriginalType(op_type) != "feed" &&
+            !GpuKernelSupportPrecision(GetOpOriginalType(op_type),
+                                       phi::DataType::FLOAT32)) {
+          for (auto* out_var_node : op_node->outputs) {
+            CHECK_EQ(out_var_node->IsVar(), true);
+            if (out_var_node->Var()->Persistable()) continue;
+            if (!VarNodeHasDtype(out_var_node)) continue;
+
+            vars_should_not_low_precision.insert(out_var_node->Var()->Name());
+          }
+        }
       }
     }
   };
@@ -449,6 +463,25 @@ void AutoMixedPrecisionPass::UpdateOpPrecision() const {
       for (auto* op_node : nodes) {
         if (op_run_low_precision_.count(op_node->Op()->Type()) == 0) continue;
 
+        for (auto* in_var_node : op_node->inputs) {
+          CHECK_EQ(in_var_node->IsVar(), true);
+          if (!VarNodeHasDtype(in_var_node)) continue;
+
+          auto* real_in_var_node = real_vars_[in_var_node->Var()->Name()];
+          if (real_in_var_node->Var()->Persistable()) continue;
+
+          if (vars_should_not_low_precision.count(
+                  real_in_var_node->Var()->Name())) {
+            op_run_low_precision_.erase(op_node->Op()->Type());
+            precision_updated = true;
+            VLOG(4) << op_node->Op()->Type()
+                    << " should not run at low precision.";
+            break;
+          }
+        }
+
+        if (op_run_low_precision_.count(op_node->Op()->Type()) == 0) continue;
+
         for (auto* out_var_node : op_node->outputs) {
           CHECK_EQ(out_var_node->IsVar(), true);
           if (!VarNodeHasDtype(out_var_node)) continue;