In order to improve the security of traditional optical image encryption and reduce the amount of data what needs to process, we propose a color image asymmetric optical encryption method based on compressed sensing and quantum logistic map, and use the compressive sensing theory and single-channel encrypted method to deal with the problem of large amount of data in the process of color image encryption. Aiming at the linear problem of the traditional optical cryptosystem, we use asymmetric optical encryption based on phase truncation fractional Fourier transform. We also use quantum logistic map to generate the random phase masks for the convenience of transmitting random phase masks. The results show that the proposed algorithm can obtain better image encryption and decryption results.