Considering the information security problems involved in the transmission and storage of satellite images, a new satellite image encryption algorithm based on chaos theory and DNA dynamic coding is proposed. Firstly, an improved infinite folding chaotic map is proposed, which broadens the chaotic interval of the original infinite folding chaotic map. Then, combined with the improved Chebyshev chaotic map and SHA-256 hash algorithm, the key stream of the encryption algorithm is generated to improve the plaintext sensitivity of the algorithm. Then, the state value of the chaotic system is used to encode the pixels after Hilbert local scrambling to realize DNA dynamic coding, which solves the weakness of being vulnerable to violent attacks caused by fewer DNA coding rules. Finally, the chaotic sequence is used to complete further chaotic encryption, to completely confuse the original pixel information, increase the randomness and complexity of the encryption algorithm, and obtain the ciphertext image. The experimental results show that the algorithm has a better encryption effect and the ability to deal with various attacks.