Aimming at the drawback of the classical total vaiational denoising model in whi ch the staircasing effect is often produced,an improved image restoration model based on adaptive second order tota l generalized variation (TGV) is proposed in this paper.In the new model,an edge indicator function is introduced in the regularization term of second order tot al generalized variation.The proposed model makes use of the advantages of the e dge indicator function that can improve the diffusion and remove the noise in th e image smooth region,and reduce the diffusion and protect the edges in the imag e non-smooth region to restore the noisy image.The adaptive second order total gneralized vairation is the regularization term in the proposed model,which can automatically balance the first order and second order derivative.So these chara cteristics make the new model preserve the edge information better and avoid the staircasin g effect while removing noise.In order to solve the proposed model effectively,t he primal-dual method is used in this paper.The experimental results show that compared with the existing congeneric algorithms,the new model removes the exist ing noise effectively and preserves the edges of image while avoiding the stairc asing effect.Therefore,the restored results are improved in both visual effects and signal to noise ratio (SNR)．