In order to detect malwares on the Android platform more effectively, we put forward a static comprehensive detection method which combines sensitive permissions with function-call graphs. Firstly, through reverse engineering, we constructed a malware graph database, including sensitive permissions and function-call graphs of numbers of malwares. Then, we used the Munkres algorithm to calculate the graph edit distance between the function-call graphs of the test sample and database at the same sensitive permissions to get the similarity of two function-call graphs, the similarity between two apps and detect malware further. The result shows that our method is highly effective in terms of a high accuracy and a low false positive rate, and it can detect more malwares when compared to the detection rate of Androguard.