The high proliferation rate of Android devices has exposed the platform to wider vulnerabilities of increasing malware attacks. Emerging trends of the malware threats are employing highly sophisticated and dynamic detection avoidance techniques. This has continued to weaken the capacity of existing signature-based detection systems in their protection against new and unknown threats. Thus, the need for effective detection approaches for unknown and novel Android malware has remained a growing challenge in the field of mobile and information security. This study therefore aimed at investigating the best performing machine learning classification algorithm for the anomaly Android malware detection, leveraging on permission-based feature sets, by conduction a performance comparison analysis between six different classification algorithms namely: Naïve Bayes, Simple Logistics, Random Forest, PART, k-Nearest Neighbours (k-NN), and Support Vector Machine (SVM). The Machine learning tool that was used for the preprocessing of the feature sets and the classification processes is WEKA 3.8.2 suite. Findings of the study showed that Random Forest had the best detection result with false alarm rate of 2.2%, accuracy of 97.4%, error rate of 2.6% and ROC Area of 99.6%. The study concluded that, using Android permission features, Random Forest and k-Nearest Neighbours recoded best performances in Android malware detection, followed by Support Vector Machine and Simple Logistics classification algorithms. Partial Decision Tree (PART) performed relatively well, while Naïve Baye recorded the least performance. Consequently, the deployment of Random Forest model and k-NN model are recommended for the development of an anomaly Android malware detection paradigm.