The point cloud registration technology for obtaining a three-dimensional digital model is widely applied in many areas. To improve the accuracy and speed of point cloud registration, a registration method based on multiscale normal vectors is proposed. The proposed registration method mainly includes three parts: the selection of key points, the calculation of feature descriptors, and the determining and optimization of correspondences. First, key points are selected from the point cloud based on the changes of magnitude of multiscale curvatures obtained by using principal components analysis. Then the feature descriptor of each key point is proposed, which consists of 21 elements based on multiscale normal vectors and curvatures. The correspondences in a pair of two point clouds are determined according to the descriptor’s similarity of key points in the source point cloud and target point cloud. Correspondences are optimized by using a random sampling consistency algorithm and clustering technology. Finally, singular value decomposition is applied to optimized correspondences so that the rigid transformation matrix between two point clouds is obtained. Experimental results show that the proposed point cloud registration algorithm has a faster calculation speed, higher registration accuracy, and better antinoise performance.