In this paper, we focus on a globally variational method to restore noisy images corrupted by multiplicative gamma noise. The problem is assumed as a regularization problem in total variation (TV) framework with data fitting term which is deduced by maximizing the a-posteriori probability density (MAP estimation). We need to evaluate the proximal operator of a data fitting term then we numerically adapt the Douglas-Rachford (DR) splitting method to solve the problem. Real images with different levels of noise were used. To validate the effectiveness of the proposed method, the proposed method was compared with other variational models. Our method shows effective noise suppression, excellent edge preservation. Measures of image quality such as PSNR (peak signal-to-noise ratio), VSNR (visual signal-to-noise ratio) and SSIM (structural similarity index) explain the proposed model's good performance.