With the prevalence of Android-based mobile devices, automated testing for Android apps has received increasing attention. However, owing to the large variety of events that Android supports, test input generation is a challenging task. In this paper, we present a novel approach and an open source tool called EHBDroid for testing Android apps. In contrast to conventional GUI testing approaches, a key novelty of EHBDroid is that it does not generate events from the GUI, but directly invokes callbacks of event handlers. By doing so, EHBDroid can efficiently simulate a large number of events that are difficult to generate by traditional UI-based approaches. We have evaluated EHBDroid on a collection of 35 real-world large-scale Android apps and compared its performance with two state-of-the-art UI-based approaches, Monkey and Dynodroid. Our experimental results show that EHBDroid is significantly more effective and efficient than Monkey and Dynodroid: in a much shorter time, EHBDroid achieves as much as 22.3% higher statement coverage (11.1% on average) than the other two approaches, and found 12 bugs in these benchmarks, including 5 new bugs that the other two failed to find.