Vehicle re-identification (Re-ID) is a challenging task that aims to recognize the same vehicle across different non-overlapping cameras. Existing attention mechanism-based methods for vehicle Re-ID often suffer from significant intra-class variation and inter-class variation due to various factors such as illumination, occlusion, viewpoint, etc. In this paper, we propose a novel network architecture for vehicle Re-ID, named Dimensional Decoupling Strategy and Non-local Relationship Network (DMNR-Net), which uses three modules to extract complementary features: global feature extraction module, non-local relationship capture module(NRCM), and dimensional decoupling module (DDS). The global feature extraction module captures complete and coarse-grained features from the whole image; the NRCM module extracts saliency information from feature maps in both spatial and channel dimensions; and the DDS decouples spatial and channel features into two branches to extract fine-grained features and focus on specific subspaces. We conduct extensive experiments on two popular publicly datasets, VeRi-776 and VehicleID, to evaluate the effectiveness of our method. The experimental results show that our DMNR-Net outperforms state-of-the-art methods by a large margin on both datasets.