diff --git a/lib/zone.ts b/lib/zone.ts
index bf4f49819..374e7941e 100644
--- a/lib/zone.ts
+++ b/lib/zone.ts
@@ -756,10 +756,22 @@ const Zone: ZoneType = (function(global: any) {
 
 
     runTask(task: Task, applyThis?: any, applyArgs?: any): any {
-      if (task.zone != this)
+      if (task.zone != this) {
         throw new Error(
             'A task can only be run in the zone of creation! (Creation: ' +
             (task.zone || NO_ZONE).name + '; Execution: ' + this.name + ')');
+      }
+      // https://github.com/angular/zone.js/issues/778, sometimes eventTask
+      // will run in notScheduled(canceled) state, we should not try to
+      // run such kind of task but just return
+
+      // we have to define an variable here, if not
+      // typescript compiler will complain below
+      const isNotScheduled = task.state === notScheduled;
+      if (isNotScheduled && task.type === eventTask) {
+        return;
+      }
+
       const reEntryGuard = task.state != running;
       reEntryGuard && (task as ZoneTask<any>)._transitionTo(running, scheduled);
       task.runCount++;
diff --git a/test/common/task.spec.ts b/test/common/task.spec.ts
index 44bcb9eb5..da1286244 100644
--- a/test/common/task.spec.ts
+++ b/test/common/task.spec.ts
@@ -873,6 +873,26 @@ describe('task lifecycle', () => {
                {toState: 'notScheduled', fromState: 'running'}
              ]);
        }));
+
+    it('task should not run if task transite to notScheduled state which was canceled',
+       testFnWithLoggedTransitionTo(() => {
+         let task: Task;
+         Zone.current.fork({name: 'testCancelZone'}).run(() => {
+           const task = Zone.current.scheduleEventTask('testEventTask', noop, null, noop, noop);
+           Zone.current.cancelTask(task);
+           task.invoke();
+         });
+         expect(log.map(item => {
+           return {toState: item.toState, fromState: item.fromState};
+         }))
+             .toEqual([
+               {toState: 'scheduling', fromState: 'notScheduled'},
+               {toState: 'scheduled', fromState: 'scheduling'},
+               {toState: 'canceling', fromState: 'scheduled'},
+               {toState: 'notScheduled', fromState: 'canceling'}
+             ]);
+       }));
+
   });
 
   describe('reschedule zone', () => {