The transmission of images via the Internet has grown exponentially in the past few decades. However, the Internet considered as an insecure method of information transmission may cause serious privacy issues. In order to overcome such potential security issues, a novel double-image visually meaningful encryption (DIVME) algorithm conjugating quantum cellular neural network (QCNN), compressed sensing (CS) and fractional Fourier transform (FRFT) is proposed in this paper. First, the wavelet coefficients of the two plain images are scrambled by the Fisher-Yates confusion algorithm, and then compressed by the key-controlled partial Hadamard matrix. The final meaningful cipher image is generated by embedding the encrypted images into a host image with the same resolution of the plain image via the FRFT-based embedding method. Besides, the eigenvalues of the plain images are utilized to generate the key stream to improve the ability of proposed DIVME algorithm to withstand the plaintext attacks. Afterwards, the plaintext eigenvalues are embedded into the alpha channel of the meaningful cipher image under control of the keys to reduce unnecessary storage space and transmission costs. Ultimately, the simulation results and security analyses indicate that the proposed DIVME algorithm is effective and can withstand multiple attacks.