In order to improve the security of quantum color images, this study proposes a novel algorithm for quantum color image encryption based on three-dimensional chaotic systems. The encrypted quantum color image is represented by the novel quantum image representation for color digital image model. The original image is first perturbed by the Arnold transform and then the RGB channel is perturbed separately from the chaotic sequence generated by the new three-dimensional chaotic system by the xor operation. Evaluation metrics such as histogram, information entropy, and correlation of neighboring pixels of the image are analyzed using MATLAB. The simulation results show that the pixel values of the encrypted image are uniformly distributed and the algorithm enhances the security of quantum color images. The specific quantum circuit diagram of the encryption algorithm is given in the paper. The superposition and entanglement properties of quantum physics greatly improve the efficiency of complex image processing algorithms, and the overall complexity of the circuit is O(n), which is efficient and implementable.