Aiming at the drawback of the total v ariational denoising model in which the staircase effect is often produced,an im proved multiplicative noise removal model based on second-order total generaliz ed variation (TGV) is proposed in this paper.In this new model,the second-order total generalized var iation is the regularization term,which can automatically balance the first order derivative and the second order deriva tive.So the proposed model makes use of the characteristics of second total generalized variation which makes the edges in the restored image preserved well and removes multiplicative noise while avoiding the staircase effect.In order to sol ve the proposed model effectively,a fast iteration algorithm is designed.In the algorithm,we first use the splitting meth od and alternating direction method to divide the primal problem into two relevant subproblems,and then the Newton meth od and primal-dual method are adopted in the respective subproblem.The comprehensive experimental results sho w that compared with the existing congeneric algorithms,the new model is more effective to filter out the existin g multiplicative noise and preserves the edges of image while avoiding the staircase effect.Therefore,the restored result s are improved in both visual effects and some quantitative indexes,such as peak signal to noise ratio.