With the widespread use of Android applications in security-sensitive scenarios, more and more Android malware has been discovered. Existing work on malware detection fail to automatically learn effective feature interactions, which are, however, the key to the success of many prediction models. In order to detect malware efficiently and accurately, in this paper, we propose Multilevel Permission Extraction, an approach to automatically identify permission interactions that are effective in distinguishing between malicious and benign applications. We then utilize the extracted information to classify malicious and benign applications by machine learning based classification algorithms. We evaluate our approach in a large data set consisting of 4,868 benign applications and 4,868 malicious applications. The experimental results show that our malware detection approach can achieve over 95.8% in accuracy, precision, recall, and F-Score. Compared with two state-of-the-art approaches, we can achieve a better malware detection rate of 97.88%.