In today's information society, image encryption technology is crucial to protecting Internet security. However, traditional image encryption algorithms have problems such as insufficient chaotic characteristics, insufficient randomness of keys, and insecure Ribonucleic Acid (RNA) encoding. To address these issues, a chaos-RNA encryption scheme that combines chaotic maps and RNA encoding was proposed in this research. The initial values and parameters of the chaotic system are first generated using the Secure Hash Algorithm 384 (SHA-384) function and the plaintext image. Next, the Lü hyperchaotic system sequence was introduced to change the image's pixel values to realize block scrambling, and further disturbance is achieved through spiral index sequence to enhance encryption effectiveness. Subsequently, to obtain the final encrypted image, the diffusion is accomplished through different RNA encoding rules and operation rules corresponding to the chaotic sequence generated by an improved one-dimensional chaotic map (1DCM). Here innovatively propose four new RNA operation rules, increasing the difficulty of decryption. Simulation results demonstrate that the normalized pixel change rate (NPCR) and the unified average changed intensity (UACI) values of the tested encrypted images were 99.61% and 33.46%, respectively. The average ciphertext entropy value in the Red Green Blue (RGB) channels were 7.9986, 7.991, and 7.991. Furthermore, this algorithm exhibits a low correlation coefficient and enhanced robustness. This encryption method effectively improves the security and reliability of image encryption compared to other similar techniques.