We propose a hyperchaotic image encryption algorithm based on plaintext information and DNA computing. Compared to the traditional permutation-diffusion structure, the proposed method enhances the relationship between pixel position, gray value, and the plaintext image. First, the algorithm’s hyperchaotic system iteratively generates multiple pseudorandom matrices and globally scrambles the image position by operating on the pseudorandom matrices and plaintext information. Then, the pseudorandom matrices and the scrambled image are encoded into DNA sequences for subsequent algebraic operations, and a new vector is constructed to modulate the sequence to obtain robust encryption performance. Finally, the processed DNA sequence is decoded and a XOR operation is applied to the binary pseudorandom sequence to obtain a final cipher image. Based on the experimental results and security analysis, the proposed algorithm not only demonstrates excellent encryption but also resists various typical attacks.