In order to overcome the limitations of traditional total variation (TV) regularization in image restoration only considering the first-order gradient characteristic of the image with the deficient ability of detail recovery and sensitivity to the noise, the total generalized variation (TGV) is applied into image deblurring. An adaptive weighted TGV image deblurring model is proposed, which can adaptively adjust the weights according to the local image structure, avoiding the staircase effect while preserving the edges of the image and suppressing the noise. In order to solve the proposed model, the adaptive weighted TGV is proposed based on primal-dual algorithm. The experimental results show that our method can obtain high quality recovery images and the solving algorithm has low time complexity and fast solving speed.