In this paper, a novel 3D image encryption based on the memristive chaotic system and RNA crossover and mutation is proposed. Firstly, the dynamic characteristics of the nonlinear system with two memristors are analyzed, including phase diagrams, Lyapunov exponential spectrums, and bifurcation diagrams. According to the merged image of three 3D images, the initial values of the memristive chaotic system are generated by SHA-256. Then the vertex coordinates are scrambled and diffused by 3D Arnold matrix and chaotic sequences. Finally, according to the dynamical encoding and decoding rules, crossover and RNA mutation are designed to confuse and diffuse the vertex coordinates. Throughout the encryption process, the Arnold matrix, RNA encoding and decoding rules, and crossover and mutation algorithms are determined by the memristive chaotic system. The experimental results verify that the proposed cryptosystem could encrypt three 3D images at the same time and resist various attacks effectively, and has good security performance.