Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two point clouds. However, the finding of reliable correspondence relies on establishing a robust and discriminative description of elements and the correct matching of corresponding elements. In this letter, we develop a coarse-to-fine registration strategy, which utilizes rotation-invariant features and a new weighted graph matching method for iteratively finding correspondence. In the graph matching method, the similarity of nodes and edges in Euclidean and feature space are formulated to construct the optimization function. The proposed strategy is evaluated using two benchmark datasets and compared with several state-of-the-art methods. Regarding the experimental results, our proposed method can achieve a fine registration with rotation errors of less than 0.2 degrees and translation errors of less than 0.1m.