This paper presents a new chaos-based image cipher using a plaintext-related permutation. The cat map and Lorenz system are employed to shuffle the positions of image pixels and generate the diffusion keystream, respectively. The control parameters of the cat map, i.e. the permutation key, are determined by the Murmur2 hash value of the original image. Owing to the avalanche property of hash functions, completely different shuffled images will be produced even if there is a tiny difference between the original ones, and it helps accelerate the diffusion process. Experimental results indicate that the proposed scheme requires only one and two cipher cycles to achieve an acceptable and a satisfactory diffusion properties, respectively, whereas two and three cipher cycles are needed by typical schemes to achieve the same properties. Thorough security analysis is carried out, and the results demonstrate the satisfactory security of the proposed scheme.