This paper presents an efficient image encryption method based on Arnold’s Cat Map and DNA computing. First, the pixel values of the image are encoded into DNA sequences, where the mapping between DNA bases and binary codes is used to achieve initial pixel information perturbation. Then, Arnold’s Cat Map is employed to perform chaotic permutation of the spatial positions of the pixels, further scrambling the image structure. The proposed method applies double encryption on both pixel values and positions, while maintaining strong reversibility, allowing the original image to be fully restored through inverse operations. Experimental validation was conducted using standard test images for encryption and decryption. The results demonstrate that this method effectively conceals the original information visually, and shows robust performance in security evaluations, including entropy analysis, correlation analysis, differential attack resistance, and cropping attack resistance. Compared to traditional encryption methods, this approach exhibits significant advantages in both complexity and security.