A color image denoising algorithm that combines multi-channel optimization and non-convex low-rank matrix approximation is proposed. The proposed improved multi-channel denoising model effectively utilizes different noise characteristics on the color channel and adaptively processes different noises in the RGB channel by introducing weight matrix. The non-convex function MCP is introduced instead of the nuclear norm to solve the problem of low rank matrix minimization. Experiments on simulations and real data sets show that the proposed multi-channel non-convex low-rank approximation minimization model is significantly better than other competing denoising algorithms.