This paper designs an efficient image hashing with a ring partition and a projected gradient nonnegative matrix factorization (PGNMF), which has rotation robustness, good discriminative capability, and secure. The key contribution is incorporating rotation-invariant secondary image with PGNMF and Security technique, which is used for the first time in image hashing to make image hash resistant to rotation as well as provide security. In addition, the used Projected Gradient NMF is fasted as compared to other NMF are approximately linearly changed by content-preserving manipulations, so as to measure hash similarity with correlation coefficient. We conduct experiments for illustrating the efficiency with 200 images. Our experiments show that the proposed hashing is robust against content-preserving operations, such as image rotation, JPEG compression, watermark embedding, Gaussian low-pass filtering, gamma correction, brightness adjustment, contrast adjustment.