Most of the existing denoising algorithms are developed for grayscale images. It is not trivial to extend them for color image denoising since the noise statistics in R, G, and B channels can be very different for real noisy images. In this paper, we propose a multi-channel (MC) optimization model for real color image denoising under the weighted nuclear norm minimization (WNNM) framework. We concatenate the RGB patches to make use of the channel redundancy, and introduce a weight matrix to balance the data fidelity of the three channels in consideration of their different noise statistics. The proposed MC-WNNM model does not have an analytical solution. We reformulate it into a linear equality-constrained problem and solve it via alternating direction method of multipliers. Each alternative updating step has a closed-form solution and the convergence can be guaranteed. Experiments on both synthetic and real noisy image datasets demonstrate the superiority of the proposed MC-WNNM over state-of-the-art denoising methods.