Images, as a crucial information carrier in the era of big data, are constantly generated, stored, and transmitted. Determining how to guarantee the security of images is a hot topic in the information security community. Image encryption is a simple and direct approach for this purpose. In order to cope with this issue, we propose a novel scheme based on eight-base DNA-level permutation and diffusion, termed as EDPD, for color image encryption in this paper. The proposed EDPD integrates secure hash algorithm-512 (SHA-512), a four-dimensional hyperchaotic system, and eight-base DNA-level permutation and diffusion that conducts on one-dimensional sequences and three-dimensional cubes. To be more specific, the EDPD has four main stages. First, four initial values for the proposed chaotic system are generated from plaintext color images using SHA-512, and a four-dimensional hyperchaotic system is constructed using the initial values and control parameters. Second, a hyperchaotic sequence is generated from the four-dimensional hyperchaotic system for consequent encryption operations. Third, multiple permutation and diffusion operations are conducted on different dimensions with dynamic eight-base DNA-level encoding and algebraic operation rules determined via the hyperchaotic sequence. Finally, DNA decoding is performed in order to obtain the cipher images. Experimental results from some common testing images verify that the EDPD has excellent performance in color image encryption and can resist various attacks.