With the development of cloud computing, more and more multimedia data is stored in the cloud. For security needs, it is often necessary to encrypt images before uploading them to the cloud for storage or computing operations. Without knowing the plaintext content of the encrypted image, in order to verify the integrity of the image information and the authenticity of the content, an image hash algorithm based on Paillier homomorphic encryption is proposed. The algorithm is mainly composed of three parts: the image owner encrypts the image, the cloud server generates a ciphertext image hash, and the receiver generates a plaintext image hash. Specifically, the image owner encrypts the image and uploads the encrypted image to the cloud server. The cloud server uses the algorithm of the Paillier cryptosystem to perform calculations of DCT and Watson human visual features in encrypted domain, and uses a key-controlled pseudo-random matrix to increase the randomness of the ciphertext hash, thereby improving the security of the hash. The receiver decrypts and analyzes the received ciphertext hash to obtain the plaintext image hash. Experimental results show that the proposed algorithm has ideal performance in terms of robustness, uniqueness, and security.