As more and more researchers explore and study quantum images, it is inevitable that the security of quantum images needs to be considered. Different models of quantum image representation have different encryption schemes. In this paper, an encryption scheme based on the cyclic shift is proposed for the MQIR image representation model that requires less quantum bits, is closer to the traditional digital image representation, and is more pervasive. Based on the idea of cyclic shift, the position information and color information of the representation model are scrambled simultaneously, which not only changes the position information of the quantum image, but also changes the statistical characteristics of the pixel grayscale value, thus improving the security of the scrambling scheme. Moreover, the encryption and decryption circuits are simple and efficient. The scheme encrypts and decrypts not only on the original image, but also on the copy-oriented image without affecting the original image. The encryption and decryption circuits are simulated on IBM Quantum experimental platform, and the correctness and effectiveness of the encryption and decryption algorithm are verified. Finally, simulation experiments are conducted on a classical computer to give the optimal number of image content-oriented cyclic shifts based on the histograms before and after the encryption and correlation coefficient. The simulation results show that the proposed quantum image encryption scheme is effective.