Alignment is a critical aspect of point cloud data (PCD) processing, and we propose a coarse-to-fine registration method based on bipartite graph matching in this paper. After data pre-processing, the registration progress can be detailed as follows: Firstly, a top-tail (TT) strategy is designed to normalize and estimate the scale factor of two given PCD sets, which can combine with the coarse alignment process flexibly. Secondly, we utilize the 3D scale-invariant feature transform (3D SIFT) method to extract point features and adopt fast point feature histograms (FPFH) to describe corresponding feature points simultaneously. Thirdly, we construct a similarity weight matrix of the source and target point data sets with bipartite graph structure. Moreover, the similarity weight threshold is used to reject some bipartite graph matching error-point pairs, which determines the dependencies of two data sets and completes the coarse alignment process. Finally, we introduce the trimmed iterative closest point (TrICP) algorithm to perform fine registration. A series of extensive experiments have been conducted to validate that, compared with other algorithms based on ICP and several representative coarse-to-fine alignment methods, the registration accuracy and efficiency of our method are more stable and robust in various scenes and are especially more applicable with scale factors.