Local feature matching is challenging due to textureless and repetitive patterns. Existing methods focus on using appearance features and global interaction and matching, while the importance of geometry priors in local feature matching has not been fully exploited. Different from these methods, in this paper, we delve into the importance of geometry prior and propose Structured Epipolar Matcher (SEM) for local feature matching, which can leverage the geometric information in an iterative matching way. The proposed model enjoys several merits. First, our proposed Structured Feature Extractor can model the relative po- sitional relationship between pixels and high-confidence anchor points. Second, our proposed Epipolar Attention and Matching can filter out irrelevant areas by utilizing the epipolar constraint. Extensive experimental results on five standard benchmarks demonstrate the superior performance of our SEM compared to state-of-the-art methods.