Aiming at convex optimization problem of undersampling image reconstruction, a new image reconstruction algorithm based on the second order Total Generalized Variation (TGV) model was proposed. In the new model, the second-order TGV semi-norm of images was used as the regularization term, which could automatically balance the first order and second order derivative. The characteristics of the TGV made the new model recover the image edge information better, smooth noise and avoid the staircasing effect. For computing the new model effectively, the orthogonal projection and the adjustment of weight threshold were presented to adaptively amend the iteration results of each step in order to obtain accurate image reconstruction results. The experimental results show that the proposed model can get better results with large value of Peak Signal-to-Noise Ratio (PSNR) and Structure SIMilarity (SSIM) in image reconstruction compared with Orthogonal Matching Pursuit (OMP) and Total Variation (TV) models.