The work aims to solve the low security problem caused by the small correlation between plaintext and chaotic system keys, and the synchronization failure of scrambling and diffusion. On the basis of combining Chebyshev and Sine mapping, a 3D chaotic mapping system (3D-CS) was constructed. A double DNA encoding image encryption algorithm based on 3D-CS chaotic system was proposed. The binary and quaternary dual DNA encoding was set. The Joseph ring transform was used to index the position of RGB layers of image encoded by binary DNA to complete both scrambling and diffusion synchronously. Then the sequence values generated by the chaotic system were processed and encoded with quaternary DNA. Finally, the two DNA sequences were added and decoded to obtain the ciphertext. Simulation experiment showed that index sequences and chaotic sequences were tested by randomness. The NPCR values of each layer of ciphertext were 99.63%, 99.61% and 99.59%, and the UACI values were 33.43%, 33.44% and 33.40%, respectively. The entropy of information were 7.9992, 7.9991 and 7.9993. Compared with other chaotic sequences, the chaotic ciphertext has some advantages over other chaotic system sequences. It can effectively improve the security of encryption algorithm and resist statistical attacks and differential attacks.