Impulse noise is one of the main causes of image degradation, low density impulse noise can be easily removed while high density impulse noise removal is more difficult. In order to effectively remove high density impulse noise and to keep edges and texture better, an algorithm based on Moreau envelope smoothing l1/total variation (l1/TV) norm model is proposed. This algorithm has advantages such as contrast and morphological invariance and absence of local blur. Since the convex objective function in l1/TV model is non-differentiable and thus difficult to solve, smoothing the total variation part by utilizing decoupled Moreau envelope is proposed. As the smoothed function which generates an iterative form of analytical solution is the differentiable tight lower bound of the original function, it is provable that they have the same solution. The simulation results show that the algorithm effectively removes noise with edges and texture kept. In addition, the combined acceleration steps are proposed to greatly improve the speed of convergence.