When using deep learning methods for point cloud registration, directly using feature similarity as the sampling basis, the samples will often be too concentrated and most of them distributed in the non-salient region such as plane, which is not conducive to the estimation of the transformation matrix. To solve this problem, an edge-aware point cloud registration algorithm is proposed. Firstly, the edge region is detected by analyzing the spatial distribution of each point in the point cloud and its neighbors. Secondly, according to the existing feature descriptors and joint learning frameworks, the sampling areas of correspondences and keypoints are limited to the edge region, so as to improve the ability of feature matching. Finally, a probabilistic sampling method based on feature similarity and saliency is used to obtain a set of well-distributed correspondences or keypoints for registration. A large number of experiments on real and synthetic datasets show that our method can make feature descriptors achieve comparable performance to existing joint learning frameworks, for the latter, sampling keypoints in the edge region can increase the registration recall by an average of 5% in the low overlap scenarios(3DLoMatch).