Abstract: A primal-dual model for image denoising is proposed based on duality principle. We theoretically analyze its equivalency with the ROF denoising model,and its structural similarity with the saddle-point optimization model. A primal-dual algorithm based on resolvent for solving the saddle-point problem is used for solving the model. To guarantee the convergence,the range of parameter is given. In terms of model's parameter selection,the regularization parameter is updated adaptively based on the Morozov's discrepancy principle which can guarantee the denoised image in the feasible set,and protect more image feature. The experiment results show that the proposed regularization parameter selection strategy is effective in improving the denoising effect. Simultaneously,the primal-dual algorithm based on resolvent can convergent rapidly.