diff --git a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
index a371ee10fe03cda86c316f3503f9cadb8c716ae5..927078bc64d8eccc4c488dc03a95c4cfb2dfbb2e 100644
--- a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
+++ b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
@@ -51,8 +51,6 @@ FeedFetchList ThreadedSSAGraphExecutor::Run(
   // together since we currently cannot overlap computation and memcpy streams.
   // Should revisit it if overlapping is available.
   std::unordered_set<OpHandleBase *> delayed_ops;
-  std::unordered_set<OpHandleBase *> blocked_by_delayed_ops;
-  std::unordered_set<VarHandleBase *> delayed_vars;
 
   auto InsertPendingVar = [&pending_vars, &ready_vars](VarHandleBase &var) {
     pending_vars.insert(&var);
@@ -122,24 +120,26 @@ FeedFetchList ThreadedSSAGraphExecutor::Run(
     InsertPendingOp(*op);
   }
 
-  auto run_all_ready_ops = [&] {
-    for (auto *op : ready_ops) {
-      if (op->IsMultiDeviceTransfer() && allow_op_delay_) {
-        delayed_ops.insert(op);
-        delayed_vars.insert(op->outputs_.begin(), op->outputs_.end());
-        ready_vars.Extend(op->outputs_);
-        continue;
-      }
+  auto run_all_ops = [&](std::unordered_set<OpHandleBase *> &set) {
+    for (auto *op : set) {
       running_ops_++;
       RunOp(&ready_vars, op);
     }
-    ready_ops.clear();
+    set.clear();
   };
 
   // Step 3. Execution
-  while (!pending_vars.empty() || !ready_ops.empty() || !delayed_ops.empty()) {
+  while (!pending_vars.empty()) {
     // 1. Run All Ready ops
-    run_all_ready_ops();
+    // Keep loop until all vars are ready.
+    //
+    // NOTE: DelayedOps have a lower priority. It will be scheduled after all
+    // ready_ops have been performed.
+    if (ready_ops.empty() && allow_op_delay_) {
+      run_all_ops(delayed_ops);
+    } else {
+      run_all_ops(ready_ops);
+    }
 
     // 2. Find ready variable
     bool timeout;
@@ -160,29 +160,16 @@ FeedFetchList ThreadedSSAGraphExecutor::Run(
         auto &deps = pending_ops[op];
         --deps;
         if (deps == 0) {
-          if (delayed_vars.find(ready_var) != delayed_vars.end()) {
-            blocked_by_delayed_ops.insert(op);
+          if (op->IsMultiDeviceTransfer() && allow_op_delay_) {
+            delayed_ops.insert(op);
           } else {
             ready_ops.insert(op);
           }
         }
       }
     }
-    // When there are no other ops to schedule, schedule buffered delayed
-    // ops and unblock other ops.
-    if (ready_ops.empty() && !delayed_ops.empty() && running_ops_ == 0) {
-      RunDelayedOps(delayed_ops);
-      delayed_ops.clear();
-      for (auto *op : blocked_by_delayed_ops) {
-        ready_ops.insert(op);
-      }
-      blocked_by_delayed_ops.clear();
-    }
-    // Keep loop until all vars are ready.
   }
   PADDLE_ENFORCE(ready_ops.empty());
-  PADDLE_ENFORCE(delayed_ops.empty());
-  PADDLE_ENFORCE(blocked_by_delayed_ops.empty());
 
   // Wait FetchOps.
   if (!fetch_ops.empty()) {
diff --git a/python/paddle/fluid/tests/unittests/test_parallel_executor.py b/python/paddle/fluid/tests/unittests/test_parallel_executor.py
index 83d22fd799eea55eedb58f93421b275985edb50b..0cd88d61e1d5456bb9267a58d832e4148e085216 100644
--- a/python/paddle/fluid/tests/unittests/test_parallel_executor.py
+++ b/python/paddle/fluid/tests/unittests/test_parallel_executor.py
@@ -206,18 +206,19 @@ class TestParallelExecutorBase(unittest.TestCase):
                                   feed_dict={}):
         main = fluid.Program()
         startup = fluid.Program()
+        startup.random_seed = 1  # Fix random seed
         with fluid.program_guard(main, startup):
             loss = method(use_feed=len(feed_dict) > 0)
             adam = fluid.optimizer.Adam()
             adam.minimize(loss)
             if memory_opt:
                 fluid.memory_optimize(main)
-
             place = fluid.CUDAPlace(0)
             startup_exe = fluid.Executor(place)
             startup_exe.run(startup)
 
-            exe = fluid.ParallelExecutor(True, loss_name=loss.name)
+            exe = fluid.ParallelExecutor(
+                True, loss_name=loss.name, allow_op_delay=allow_op_delay)
             if batch_size is not None:
                 batch_size *= fluid.core.get_cuda_device_count()
             begin = time.time()