The goal of feature matching is to establish accurate correspondences between feature points in different images depicting the same scene. To address the polymorphism of local structures, the authors propose a mismatch removal method using bilateral local–global structural consistency. This method incorporates the problem of mismatch removal into the framework of graph matching, constructs a global affinity matrix using local structural similarity and global affine transformation consistency, and optimizes it using a constrained integer quadratic programming method. To comprehensively describe the local structure, the signature quadratic form distance (SQFD) is used to measure the consistency of the neighbourhood structure. Specifically, the weights of edges are constructed based on the SQFD of the local structure, while the matching correctness of nodes and edges between the two graphs is described using local vector similarity. Furthermore, the consistency of the global affine transformation is evaluated by assessing the consistency of the local neighbourhood affine transformation between different corresponding point pairs. In estimating the local affine transformation, a bilateral correction is performed using a total least‐squares (TLS) algorithm to measure the similarity of nodes between the two different graphs. Experimental results demonstrate that the proposed algorithm outperforms state‐of‐the‐art methods in terms of accuracy and effectiveness.