With the continuous improvement and optimization of security monitoring networks, vehicle Re-Identification (Re-ID) becomes an emerging key technology in the development of intelligent visual surveillance systems. Due to the influence of viewpoint variation and fine-grained differences, vehicle Re-ID is still a research topic worth investigating. To alleviate above problems, a novel end-to-end framework named Unified Relational Reasoning Network (URRNet) is proposed in this paper, which integrates global features with local features to obtain better recognition accuracy. For the proposed framework, to understand the overall semantics of the image, an algorithm based on the global feature graph-structure learning is designed. The pixel-level feature maps are transformed to the node features of graph in the interactive space by projection, then graph reasoning is performed by using the graph convolutional network to improve the representation of global features. Moreover, an algorithm based on multi-scale local feature relational reasoning is designed. Using keypoint and viewpoint to obtain the multi-scale partial characteristics of the vehicle, and the vehicle multi-view features are learned from the single-view vehicle images through relational reasoning and attention mechanism. The two algorithms are combined to obtain the overall model, which not only preserves the details of the vehicle, but also effectively solves the problem of viewpoint variation. Comprehensive experimental results on two public datasets (VeRi-776 and VehicleID) indicate that the proposed URRNet can practically improve the model's representation ability and generalization ability, which is comparable to the state-of-the-art vehicle Re-ID methods.