Point cloud registration plays an important role in three-dimensional laser scanning technology as it affects modeling quality directly. The iterative closest point (ICP) algorithm is widely used in point cloud registration because it can register the point cloud automatically and accurately. But the ICP algorithm is complex in time and space, slow convergence and easy incorrect matching. The ICP algorithm and the curvature extremum algorithm are combined as a new algorithm to process point clouds with apparent curvature features. Experiments are conducted concerning effect of convergence efficiency, robustness and quality of initial data on the new algorithm, and the results of the classic ICP algorithm and other modified ICP algorithms are compared. The results show that the proposed algorithm has high convergence efficiency for point clouds with apparent curvature features and good convergence stability for worse initial data.