Low-rank tensor representation-based multi-view clustering has become an efficient method for data clustering due to the robustness to noise and the preservation of the high order correlation. However, existing algorithms may suffer from two common problems: (1) the local view-specific geometrical structures and the various importance of features in different views are neglected; (2) the low-rank representation tensor and the affinity matrix are learned separately. To address these issues, we propose a novel framework to learn the Graph regularized Low-rank Tensor representation and the Affinity matrix (GLTA) in a unified manner. Besides, the manifold regularization is exploited to preserve the view-specific geometrical structures, and the various importance of different features is automatically calculated when constructing the final affinity matrix. An efficient algorithm is designed to solve GLTA using the augmented Lagrangian multiplier. Extensive experiments on six real datasets demonstrate the superiority of GLTA over the state-of-the-arts.