The shape and structure of nonspherical objects are complex, and it is easy to mismatch when using point clouds for direct registration. Aiming at this problem, the geodesic distance on the manifold is introduced here along with the actual geometric shape of the object. Additionally, the three-dimensional (3D) point cloud registration problem is converted into a clustering problem, and a multisite cloud registration method based on manifold clustering is proposed. First, the 3D point cloud after rough registration was divided into several clusters. Then, the geodesic distance was used as the basis of cluster division to update the cluster center while updating the rigid transformation simultaneously. The process was repeatedly iterated to obtain the final registration result. Finally, in the registration process, the geodesic distance matrix calculation easily generated a computational consumption, and the thermal gradient method was applied to transform the traversal process of point sets in space into a Poisson equation solution to improve efficiency and complete the multisite cloud registration. Experimental results on Bunny, Dragon, and other point cloud data in the Stanford University public dataset show that the proposed method can effectively improve the registration accuracy of nonspherical objects by 20%-30%.