As the application of multimedia technology intensifies recently, more and more attention has been paid to privacy protection in image data. The interest in DNA-based image encryption techniques is increasing due to their high parallelism and large storage capacity. However, there are only few types of operations in existing DNA encryption methods and many of them are susceptible to chosen-plaintext attacks. To solve these problems, this paper proposes a novel image encryption algorithm based on a new DNA sequence operation and hyperchaotic system. Firstly, SHA-256 algorithm is used in conjunction with chaotic systems to generate plaintext-related random sequences. Secondly, the plain image is decomposed into RGB channels and encoded into DNA matrices. Thirdly, a new DNA operation called DNA triploid mutation (DNA-TM) is introduced to achieve cryptographic conversion of DNA bases. Furthermore, after decoding three DNA matrices, row-column permutation and pixel diffusion are employed to fuse the image. The experimental results demonstrate that our encryption approach is secure, with an average information entropy of 7.9972. In addition, the security analysis reveals that our scheme can resist differential attacks, plaintext attacks, noise attacks and occlusion attacks.