Considering the demand of detecting Android malware and the redundancy of permission properties, a fast scheme was proposed to detect malware from the perspective of permission correlation. To eliminate the redundant permissions, Chi-square test was used to compute the influence of the permission on the classification results. Then some representative permissions were selected on the basis of permission clustering to further reduce redundancy. Finally an improved Naive Bayesian classification based on the weights of different permissions was proposed to classify the software. Results of the experiments conducted on 2000 software samples show that the miss rate of malware detection is 10.33% and the overall prediction accuracy is 88.98%. Experiments indicate that this scheme is capable of detecting malware on Android platform by using a few permission properties, which can provide a reference for further analysis and judgment.