Orthogonal moments and their invariants to similarity transformations for monochrome and gray-scale images are widely used in many pattern recognition and image processing applications. Quaternion orthogonal moments are used with color images. Recently, the multi-channel framework is proposed as a successful alternative of the quaternion orthogonal moments in representation and recognition of the color images. In this paper, a new set of multi-channel orthogonal moments and their invariants to rotation, scaling and translation (RST) is proposed for color image representation and recognition. The proposed multi-channel moments are based on the orthogonal radial substituted Chebyshev functions. The multi-channel orthogonal radial substituted Chebyshev moments (MORSCMs) are defined in polar coordinates over a unit circle. An accurate kernel-based method is utilized for accurate computation of the MORSCMs. A series of experiments is performed to validate this new set of multi-channel moments and compare its performance with the existing quaternion and multi-channel orthogonal moments. The obtained results ensure the superiority of the proposed MORSCMs over all existing moments in representation and recognition of the color images.