To improve the registration efficiency and accuracy of three-dimensional laser scanning point cloud, we propose a point cloud registration algorithm based on l p space mechanics model. In the algorithm, the center of gravity of the sets data is calculated first, and two point clouds are moved to the same coordinate system with the center as the origin through gravity-centralizing. The complex point sets to be registered are represented as three eigenvectors respectively with the space mechanics model. Then, the singular value decomposition method is used to solve the rigid body transformation rotation matrix according to the corresponding relationship between two point sets’ eigenvectors. Finally, with the initial registration result, the improved iterative closest point (ICP) algorithm leads to perfect registration. The proposed algorithm can deal with disordered and scattered cloud sample. Compared with the classic ICP algorithm, the proposed method increases efficiency by 72% for the Bunny point cloud and is 4 times faster for Dragon scanning data. Experimental results indicate that the proposed algorithm has a fast convergence rate and good effect.