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Most image encryption methods based on Rubik’s cube scrambling adopt the idea of cyclic shift or map the image pixels to the cube surface, not fully considering the cube’s three-dimensional (3D) properties. In response to this defect, we propose a mixed chaotic color image encryption method based on parallel rotation scrambling in 3D Rubik’s cube space. First, a seven-dimensional hyperchaotic system is introduced to generate chaotic pseudo-random integer sequences. Then, a proven lemma is applied to preprocess the red (R), green (G), and blue (B) channels of the plain image to realize the first diffusion. Next, the chaotic integer sequence is employed to control Arnold transformation, and the scrambled two-dimensional (2D) pixel matrix is converted into a 3D matrix. Then, the 3D cube is scrambled by dynamically selecting the rotating axis, layer number, and angle through the chaotic integer sequence. The scrambled 3D matrix is converted into a 2D matrix, realizing the second diffusion via exclusive OR with the chaotic matrix generated by logistic mapping. Finally, the matrices of the R, G, and B channels are combined into an encrypted image. By performing the encryption algorithm in reverse, the encrypted image can be decrypted into the plain image. A simulation analysis shows that the proposed method has a larger key space and exhibits stronger key sensitivity than some existing methods.