Existing object re-identification methods usually utilize backbone networks developed based on classification tasks to obtain the final object features. However, these backbone networks lack a unique mechanism to explore discriminative feature representation and handle rich scale changes. For that, a novel hierarchical similarity graph module (HSGM) is proposed to relieve the conflict of backbone networks and mine the discriminative features. Specifically, the proposed HSGM constructs a rich hierarchical graph to explore the pairwise relationships among global-local and local-local. Then, in each hierarchical graph, the HSGM regards local features extracted from different locations as nodes and utilizes the similarity scores between nodes to construct a similarity graph. During the HSGM's propagation, a learnable parameter is reweighted at each spatial position to optimize the correlation between adjacent nodes. Besides, the HSGM can be readily inserted into backbone networks at any depth to improve object discrimination. Extensive experiments on two large-scale object datasets (i.e., VeRi776 and Market-1501) demonstrate that the proposed HSGM is superior to state-of-the-art object re-identification approaches.