Inspired by the great success achieved by CNN in image recognition, view-based methods applied CNNs to model the projected views for 3D object understanding and achieved excellent performance. Nevertheless, multi-view CNN models cannot model the communications between patches from different views, limiting its effectiveness in 3D object recognition. Inspired by the recent success gained by vision Transformer in image recognition, we propose a Multi-view Vision Transformer (MVT) for 3D object recognition. Since each patch feature in a Transformer block has a global reception field, it naturally achieves communications between patches from different views. Meanwhile, it takes much less inductive bias compared with its CNN counterparts. Considering both effectiveness and efficiency, we develop a global-local structure for our MVT. Our experiments on two public benchmarks, ModelNet40 and ModelNet10, demonstrate the competitive performance of our MVT.