A new chaotic image encryption scheme based on fractional order wavelet decomposition is proposed in this paper. First, a three-stage fractional-order wavelet decomposition is performed on the image, and the high-frequency component and low-frequency component are obtained after the decomposition. A chaotic system is used to dislocate the high-frequency components, and a fractional matrix model is constructed to dislocate the low-frequency components. After that, quantum encoding is performed on the scrambled image and the Arnold transform is performed to obtain the final scrambled result. Finally, the final encryption result is obtained by iteratively obtaining the M4 key matrix and diffusing the quantum image after permutation. The simulation experiment and numerical analysis show that the encryption method proposed in this paper has excellent security.