In this article, a color image chunking encryption algorithm based on DNA and compound chaotic systems is proposed. In the algorithm proposed in this article, two new chaotic systems are designed, the One Dimensional Logistic and Tent Mapping (1D-LATM) and the Two Dimensional Logistic and Sine mapping (2D-SALM). Firstly, associating 2D-SALM chaotic system with plain generates chaotic sequences to improve plain sensitivity. Secondly, splitting the color image into three two-dimensional matrices. And the matrices are filled with zeros as required. Thirdly, the chunking operation is performed on the matrix after the complementary zeros to increase the speed of running. Fourthly, DNA manipulations are performed on the image blocks, meanwhile, the rules are determined by chaotic sequences. The sequences are produced by 2D-SALM and 1D-LATM chaotic systems. Finally, we perform the random scrambling operation and the cyclic shift diffusion operation. The cryptogenerator generates two matrices through the 2D-SALM chaotic system. These matrices used in scrambling and diffusion operations. Through the above operation, we get the ultimate color encrypted picture. The outcomes of experimental and analyses of algorithm indicate that this algorithm has excellent encryption effectiveness, well safety and fast running speed. The algorithm proposed in this paper takes only 0.68 s to encrypt an image of size 256 × 256 and 1.32 s to encrypt an image of size 512 × 512. NPCR and UACI are 99.6095%, 33.4631%. The information entropy is 7.9983.