In many applications related to point clouds, registration is an inevitable step when processing point cloud data. The registration methods performed by local shape descriptor (LSD) are computationally efficient and suitable for different scenes, but they achieve low registration accuracy due to the limited performance of the LSD. For this reason, a novel LSD is designed for terrestrial point clouds. First, a simple yet efficient local reference frame (LRF) is developed. The LRF is calculated by the robust normal vector and constant vector, so it has high repeatability. This increases the robustness of the descriptor. Then, the local neighborhood information is encoded based on the LRF in 3-D space. The voxel centers are used to compute the feature descriptor. This increases the descriptiveness of the descriptor because the voxel centers can well preserve the local information. Thus, the proposed LSD is highly descriptive and strongly robust. Based on the novel LSD, a registration method is given. The proposed LSD makes the registration method have high accuracy. Also, the proposed LRF can improve the performance of the correspondence selection, which is an important process in an LSD-based registration method. The experiments performed on the point clouds of different scenes well illustrate that our LRF method has significantly better repeatability and robustness in comparison with other LRF methods. The proposed LRF can largely improve the performance of the descriptor. Our LSD also has significantly better descriptiveness and robustness compared to the other descriptors. As a result, our registration method achieves high accuracy and good time efficiency due to the proposed LSD. The code will be available at https://github.com/taowuyong?tab=repositories after publication.