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The establishment of point‐to‐point correspondence between point clouds is called three‐dimensional point matching, which is widely used in computer vision, computer graphics, robotics and other fields. When the scale of source point cloud and target point cloud are different, it brings great difficulties to obtain the satisfactory matching result. Therefore, the article proposes a registration algorithm to solve this problem effectively. First, we construct a multi‐scale space related to Gaussian standard deviation. Second, we use a topological similarity of two directed trees constructed by feature points coming from two point clouds for fuzzy matching. Finally, we use local matching and global matching methods to find the corresponding relationship between patches in multi‐scale space. We find the feature correspondence of different scales in multi‐scale space and get the scale factor. Our method improves the accuracy of matching by eliminating mismatch caused by descriptor matching and local geometry matching. We show great performance of our approach by conducting extensive experiments, which outperforms other state‐of‐the‐art methods, in particular, it provides a valuable tool for point cloud registration.