A novel cryptosystem of color images is proposed. We defined a multi-channel orthogonal Gegenbauer moments with fractional order (FrMGMs) in Cartesian coordinates and then combined the FrMGMs with the 2D logistic-sine map. The proposed color image encryption method has three main steps in this process. The first step is confusion, where image pixels’ values are changed based on a 2D logistic-sine map to reconstruct the scrambled image. In the second step, the key is generated, which is used in encryption. The key is produced by combining the logistic map and the multi-channel Gegenbauer moments with fractional order. We used the original image to set the logistic map’s initial condition. In the third step, the scrambled image is diffused using the key to obtain an encrypted image. The experiments’ results and the security analysis show that the proposed technique has an extensive keyspace, high key sensitivity, and good encryption effect and can be judged robust against common security attacks.