With the rapid development of android smart terminals, android applications are exhibiting explosive growth. However, there remains a challenging issue facing android system, a malicious application may broadcast user's private information. In this paper, we propose a Naive Bayesian-based approach for analyzing private information leakage under the android broadcast mechanism, which calls BRbysA. Firstly, broadcast actions registered in manifest.xml are picked up statically by keyword matching technique. Secondly, with the Xposed framework, the broadcast actions specified at run time are discovered by hooking broadcast callback onReceive() function. Combining the above two ways, we can capture all real-time broadcast actions in an android application. Thirdly, we adopt Naive Bayesian learning algorithm, all broadcast actions which involved in users' privacy leakage are analyzed and classified. Finally, we evaluate the proposed approach by using the dataset from Drebin and Google Play.