As a prerequisite for many 3D visualization tasks, point cloud registration has a wide range of applications in 3D scene reconstruction, pose estimation, navigation, and remote sensing. However, due to the limited overlap of point clouds, the presence of noise and the incompleteness of the data, existing feature-based matching methods tend to produce higher outlier matches, thus reducing the quality of the registration. Therefore, the generation of reliable feature descriptors and the filtering of outliers become the key to solving these problems. To this end, we propose a multi-local-to-global registration (MLGR) method. First, in order to obtain reliable correspondences, we design a simple but effective network module named the local geometric network (LG-Net), which can generate discriminative feature descriptors to reduce the outlier matches by learning the local latent geometric information of the point cloud. In addition, we propose a multi-local-to-global registration strategy to further filter outlier matches. We compute the hypothetical transformation matrix from local patch matches. The point match evaluated as an inlier under multiple hypothetical transformations will receive a higher score, and low-scoring point matches will be rejected. Finally, our method is quite robust under different numbers of samples, as it does not require sampling a large number of correspondences to boost the performance. The numerous experiments on well-known public datasets, including KITTI, 3DMatch, and ModelNet, have proven the effectiveness and robustness of our method. Compared with the state of the art, our method has the lowest relative rotation error and relative translation error on the KITTI, and consistently leads in feature matching recall, inlier ratio, and registration recall on 3DMatch under different numbers of point correspondences, which proves the robustness of our method. In particular, the inlier ratio is significantly improved by 3.62% and 4.36% on 3DMatch and 3DLoMatch, respectively. In general, the performance of our method is more superior and robust than the current state of the art.