Point cloud registration is a key problem for robotics, computer vision, and other applications. Previous global registration algorithms are sensitive to noises or partial occlusion, while local registration algorithms are highly dependent on initial angles. To solve these problems, we propose CentroidReg, a global-to-local framework for partial point cloud registration, desensitizing noises and initial angles. The partial point clouds have consistent global information (the centroid of the complete 3D shape) and local surface structures, which motivates us to combine rotation-invariant global and local information for correspondence generating. To estimate the centroid of the complete 3D shape for partial point clouds, we propose the CentroidNet with centroid voting and maximum likelihood estimation (MLE) aggregation. Then, we use the proposed RegistrationNet to extract hybrid rotation-invariant features (HRIF) combining global information of the entire 3D shape and local structures in the local area to describe each point. Furthermore, we propose the Reliable Correspondence Generating (RCG) module to generate correspondences in the overlapping area. Finally, a weighted differentiable singular value decomposition (SVD) step is performed to estimate the final rigid transformation. The proposed framework presents state-of-the-art performance on partial point cloud registration. Experiments show that our method is robust to initial angles and noises.