diff --git a/luigi/worker.py b/luigi/worker.py
index 43e5dc0c0f..71cefe6a0c 100644
--- a/luigi/worker.py
+++ b/luigi/worker.py
@@ -209,12 +209,7 @@ def run(self):
                 with self._forward_attributes():
                     new_deps = self._run_get_new_deps()
                 if not new_deps:
-                    if not self.check_complete_on_run:
-                        # update the cache
-                        if self.task_completion_cache is not None:
-                            self.task_completion_cache[self.task.task_id] = True
-                        status = DONE
-                    elif self.check_complete(self.task):
+                    if not self.check_complete_on_run or self.check_complete(self.task):
                         status = DONE
                     else:
                         raise TaskException("Task finished running, but complete() is still returning false.")
diff --git a/test/worker_test.py b/test/worker_test.py
index 750f05b933..99ff6994e4 100644
--- a/test/worker_test.py
+++ b/test/worker_test.py
@@ -506,9 +506,9 @@ def run(self):
             w.run()
             # the complete methods of a's yielded first in b's run method were called equally often
             self.assertEqual(b0.complete_count, 1)
-            self.assertEqual(a0.complete_count, 2)
-            self.assertEqual(a1.complete_count, 2)
-            self.assertEqual(a2.complete_count, 2)
+            self.assertEqual(a0.complete_count, 3)
+            self.assertEqual(a1.complete_count, 3)
+            self.assertEqual(a2.complete_count, 3)
 
         # test with disabled cache_task_completion
         with Worker(scheduler=self.sch, worker_id='2', cache_task_completion=False) as w: