A new method of image encryption and decryption is proposed, where the encryption process is different from the decryption and the encryption keys are also different from the decryption keys. The encryption is nonlinear for the sake of security enhancement while the decryption is linear. Two original images are combined as a complex amplitude image and encrypted based on classical double random phase encoding (DRPE) and phase-truncated Fourier transform (PTFT). Two private keys are generated in the encryption process and the decryption can be performed by the double random phase encoding scheme. Compared with the classical DRPE and PTFT-based single-image encryption, the proposed method is more secure and has resistance against on the specific attack that is based on two-step amplitude-phase retrieval algorithm. Numerical simulations are carried out to demonstrate the validity and security of the proposed scheme.