We present a new method of primate face recognition, and evaluate this method on several endangered primates, including golden monkeys, lemurs, and chimpanzees. The three datasets contain a total of 11,637 images of 280 individual primates from 14 species. Primate face recognition performance is evaluated using two existing state-of-the-art open-source systems, (i) FaceNet and (ii) SphereFace, (iii) a lemur face recognition system from literature, and (iv) our new convolutional neural network (CNN) architecture called PrimNet. Three recognition scenarios are considered: verification (1:1 comparison), and both open-set and closed-set identification (1:N search). We demonstrate that PrimNet outperforms all of the other systems in all three scenarios for all primate species tested. Finally, we implement an Android application of this recognition system to be assist primate researchers and conservationists in the wild for individual recognition of primates.