LiDAR offers a wide range of uses in autonomous driving, remote sensing, urban planning, and other areas. The laser 3D point cloud acquired by LiDAR typically encounters issues during registration, including laser speckle noise, Gaussian noise, data loss, and data disorder. This work suggests a novel Student’s t-distribution point cloud registration algorithm based on the local features of point clouds to address these issues. The approach uses Student’s t-distribution mixture model (SMM) to generate the probability distribution of point cloud registration, which can accurately describe the data distribution, in order to tackle the problem of the missing laser 3D point cloud data and data disorder. Owing to the disparity in the point cloud registration task, a full-rank covariance matrix is built based on the local features of the point cloud during the objective function design process. The combined penalty of point-to-point and point-to-plane distance is then added to the objective function adaptively. Simultaneously, by analyzing the imaging characteristics of LiDAR, according to the influence of the laser waveform and detector on the LiDAR imaging, the composite weight coefficient is added to improve the pertinence of the algorithm. Based on the public dataset and the laser 3D point cloud dataset acquired in the laboratory, the experimental findings demonstrate that the proposed algorithm has high practicability and dependability and outperforms the five comparison algorithms in terms of accuracy and robustness.