Recently, bit-level permutation strategy in chaotic image cryptosystem has been studied extensively due to its pixel value mixing effect. However, the efficiency of such a cryptosystem suffers from its high computational complexity, since more chaotic state variables are required to shuffle the bits rather than pixels. Besides, there exists computational redundancy when ciphering some special images using conventional approaches. To promote the efficiency, a novel bit-level chaotic image cipher based on lookup table is proposed in this paper. Accordingly, a sequential addition operation is introduced before the bit-level permutation for the purpose of reducing the permutation redundancy. Moreover, the diffusion in a cross-reverse manner is also contributed to the speed acceleration. On the other hand, a plaintext-related permutation mechanism is implemented in the lookup table construction to enhance the security of the proposed cryptosystem. Simulation results and analyses show that the proposed scheme is efficient while maintaining high security performance.