Recently, despite the promising progress having been achieved, most mismatch removal methods only consider the connection relationships of feature matches in a single neighborhood, and ignore their relationships between different neighborhoods, which will lead to the unavailability of local topological structure for feature matching. In this paper, we propose a novel robust Local Neighbor Propagation on Graphs based mismatch removal (LNPG) method for robust feature matching. LNPG starts from a novel neighborhood graph construction strategy, which leverages both the spatial and the residual information to preserve the local neighborhood structures of potential inliers. Subsequently, LNPG incorporates local neighbor propagation into the graph to enhance connection relationships of the data in different neighborhoods, by using the path-based similarity measurement and the adaptive graph partition. In addition, LNPG includes a novel consistency-filtering-based clustering algorithm, which introduces a reliable neighborhood consistency measure function and an effective cluster merging criterion for robust clustering. Overall, LNPG not only effectively distinguishes inliers from outliers, but also reliably classifies inliers into different transformation models between pairs of images. Extensive experiments on publicly available datasets show the superiority of our LNPG in comparison with other state-of-the-art methods.