The work aims to propose image denoising method with blind source separation based on convex hull optimization in consideration of the problem of removing Gaussian white noise and impulse noise from a image simultaneously for a lot of outliers in the noisy image. This proposed method treated the mixed noise and the clean image as two source signals of a noisy image. A model of blind source separation was built according to additive relationship between the mixed noise and the clean image in the noisy image. The convex hull optimization method was adopted to construct the affine hull of source signals (those were the extreme points of convex hull). Then, a clean image was separated from two noisy images by minimizing the projection error of the affine hull onto convex hull (the noisy image) for the purpose of removing mixed noise and recovering the clean image. According to the experimental results, peak signal-to-noise ratio (PSNR) value and mean structure similarity index measurements (MSSIM) value of the denoised images in the proposed method were respectively over 39.9129 dB and 0.9 even if the Gaussian and impulse mixed noise was very strong. Results of denoising experiments show that the proposed method has good performance in removing the Gaussian and impulse mixed noise and recovering the clean image from the perspective of blind source separation.