Vehicle re-identification is attracting an increasing amount of attention in intelligent transportation and is widely used in public security. In comparison to person re-identification, vehicle re-identification is more challenging because vehicles with different IDs are generated by a unified pipeline and cannot only be distinguished based on the subtle differences in their features such as lights, ornaments, and decorations. In this paper, we propose a local feature-aware Siamese matching model for vehicle re-identification. A local feature-aware Siamese matching model focuses on the informative parts in an image and these are the parts most likely to differ among vehicles with different IDs. In addition, we utilize Siamese feature matching to better supervise our attention. Furthermore, a perspective transformer network, which can eliminate image deformation, has been designed for feature extraction. We have conducted extensive experiments on three large-scale vehicle re-ID datasets, i.e., VeRi-776, VehicleID, and PKU-VD, and the results show that our method is superior to the state-of-the-art methods.