Transformer-based general visual geometry frameworks have shown promising performance in camera pose estimation and 3D scene understanding. Recent advancements in Visual Geometry Grounded Transformer (VGGT) models have shown great promise in camera pose estimation and 3D reconstruction. However, these models typically rely on ground truth labels for training, posing challenges when adapting to unlabeled and unseen scenes. In this paper, we propose a self-supervised framework to train VGGT with unlabeled data, thereby enhancing its localization capability in large-scale environments. To achieve this, we extend conventional pair-wise relations to sequence-wise geometric constraints for self-supervised learning. Specifically, in each sequence, we sample multiple source frames and geometrically project them onto different target frames, which improves temporal feature consistency. We formulate physical photometric consistency and geometric constraints as a joint optimization loss to circumvent the requirement for hard labels. By training the model with this proposed method, not only the local and global cross-view attention layers but also the camera and depth heads can effectively capture the underlying multi-view geometry. Experiments demonstrate that the model converges within hundreds of iterations and achieves significant improvements in large-scale localization. Our code will be released at https://github.com/X-yangfan/GPA-VGGT.