Abstract Aiming at the problem that insufficient complexity of ordinary multi-dimensional chaotic systems and the cumbersome design of encryption algorithms without excellent encryption effects. This paper constructs a four-dimensional hyperchaotic system with high Lyapunov exponent and complex dynamic behavior. We designed an encryption algorithm based on point mutation, mutation diffusion, and folding mutation in DNA mutations. During the encryption process, we perform point mutation transformation on the entire base sequence, then spread the mutations one by one starting from the second base of the sequence, and finally flip every four base sequences according to folding mutations. The images encrypted by this algorithm have a uniform grayscale histogram, high information entropy, and high key sensitivity. It can resist exhaustive attacks, noise attacks, cropping attacks, and differential attacks, and have a fast encryption speed.