Abstract: In order to remove the noise of image based on total variation, the denoising problem was converted to optimization problem. Semi-smooth Newton method incorporated by generalized minimum residual method was used to solve the associated optimization problem and non-symmetric linear equations. After theoretical analysis and experimental verification, a great deal of feasible data of removal noise experiment for 1-D signal and 2-D image were obtained by different methods. The results show that semi-smooth Newton method incorporated by generalized minimum residual method converges faster than that incorporated by preconditioned conjugate gradients method and alternating direction method of multipliers algorithm. The proposed method can remove the noise of image effectively.