In the task of vehicle re-identification (Re-ID), joint extraction of global and local information has become the mainstream approach. However, many Re-ID models only focus on the richness of local information while neglecting completeness. To address this issue, an algorithm based on relationship fusion and feature decomposition is proposed in this paper. The algorithm starts from the spatial and channel dimensions, dividing the features extracted by the backbone network along the vertical, horizontal, and channel dimensions. Firstly, to better highlight the foreground region of the vehicle, a mixed attention module (MAM) is proposed. Then, to explore rich feature information in the spatial dimension while making the network pay attention to more complete regions of interest, graph-based relation fusion is designed for the segmented features in the vertical and horizontal directions. To endow the network with the ability to capture more discriminative information, feature decomposition is implemented on the segmented local features in the channel direction. Finally, vehicle Re-ID is achieved through the joint effect of the features extracted from the global branch and the robust features from the local branches. Experimental results demonstrate that the proposed algorithm achieves state-of-the-art performance on two popular vehicle Re-ID datasets.