Point cloud registration is widely used in autonomous driving, SLAM, and 3D reconstruction, and it aims to align point clouds from different viewpoints or poses under the same coordinate system. However, point cloud registration is challenging in complex situations, such as a large initial pose difference, high noise, or incomplete overlap, which will cause point cloud registration failure or mismatching. To address the shortcomings of the existing registration algorithms, this paper designed a new coarse-to-fine registration two-stage point cloud registration network, CCRNet, which utilizes an end-to-end form to perform the registration task for point clouds. The multi-scale feature extraction module, coarse registration prediction module, and fine registration prediction module designed in this paper can robustly and accurately register two point clouds without iterations. CCRNet can link the feature information between two point clouds and solve the problems of high noise and incomplete overlap by using a soft correspondence matrix. In the standard dataset ModelNet40, in cases of large initial pose difference, high noise, and incomplete overlap, the accuracy of our method, compared with the second-best popular registration algorithm, was improved by 7.0%, 7.8%, and 22.7% on the MAE, respectively. Experiments showed that our CCRNet method has advantages in registration results in a variety of complex conditions.