In this work, a new method for robust image hashing is presented. The objectives of image hash are robustness and uniqueness. Exact Gaussian–Hermite moments and their invariants are used to extract highly accurate features for grey-scale images. The hash value is estimated by the sender from the features of the given image and then appended to the image to be sent. On the other hand, the authenticity of the received image has been checked by decrypting the hash value at the receiver side. To increase the level of security, a pre-shared key is used between the sender and the receiver. This process is to encrypt the hash value using a secret key before attaching with the image and then transmitting it. The similarity between different hashes is calculated by using Euclidean distance. Numerical simulation ensures the robustness of the proposed method against different kinds of attacks and preserves the image content. Hash different images exhibit very low collision probability which proves the suitability of the proposed method for robust image hash. The proposed method is compared with the existing hash methods where the obtained results clearly show the superiority of the proposed method