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A novel image encryption algorithm based on delay induced hyper-chaos (hyper-chaotic multi-attractors Chen system with time delay, HCMACS-TD), Arnold map and Multi-shift cipher function is proposed. To prevent private images from being stolen or used by unauthorized accesses, protecting images is very important. HCMACS-TD generating by linear time delay feedback, which possesses more than one positive Lyapunov exponent, the infinite dimensional, multi-attractors, and a wider chaotic parameter range is used in image encryption algorithm. Arnold map is used to complete the shuffle of the image and the multi-shift cipher function is used to encrypt the shuffled and confused image. In addition, the shuffled image except the first pixel as the initial element of the confusion process, enhances the relationship between the encrypted image and the original image. The performances of the proposed image encryption algorithm are evaluated, and the results show that the proposed image encryption algorithm has considerable advantages over some existing algorithms.