Encryption based on compression can provide compression and encryption in a single step, in which redundancy is removed by compression and security is guaranteed by encryption. A novel secure arithmetic coding scheme based on order-1 Markov model is proposed in this paper, and it is applied to image encryption where images can be transmitted securely on the Internet and the proposed algorithm significantly improve the compression efficiency of coding. Experimental results and security analyses indicate that, the algorithm can not only resist existing attacks based on arithmetic coding, but also be immune to other cryptanalysis.