In order to segment an image into foreground and background and overcome the staircase effect often caused by the total variation (TV) segmentation model, we propose a new image foreground and background segmentation model based on the second order total generalized variation (TGV). To improve the quality of image segmentation, an edge indicator function is introduced to the regularization term of the second order TGV-based image foreground and background segmentation model, which can reduce the diffusion to preserve image edge features in image edge regions, and enhance the diffusion to remove impulse noise and overcome the staircase effect in image smooth regions. Then, in order to highlight the foreground information of the image, we mark the foreground information of the image with a rectangular frame and perform distance mapping on the pixels inside the frame, outside of the frame, and on the edges. In addition, according to the energy minimization principle, the distance mapping function is introduced into the data item of the second-order TGV model so that the total energy of the model can be smaller. Finally, we propose a primal-dual segmentation method to solve the proposed model effectively. Experimental results show that the proposed model can not only avoid staircase effect, but also keep the edge information of the image and reduce the total energy of the model. The segmented image has a better visual effect.