This paper presents a robust and secure image hash algorithm. The algorithm extracts robust image features in the Radon transform domain. A randomization mechanism is designed to achieve good discrimination and security. The hash value is dependent on a secret key. We evaluate the performance of the proposed algorithm and compare the results with those of one existing Radon transform-based algorithm. We show that the proposed algorithm has good robustness against content-preserving distortion. It withstands JPEG compression, filtering, noise addition as well as moderate geometrical distortions. Additionally, we achieve improved performance in terms of discrimination, sensitivity to malicious tampering and receiver operating characteristics. We also analyze the security of the proposed algorithm using differential entropy and confusion/diffusion capabilities. Simulation shows that the proposed algorithm well satisfies these metrics.