Comparison of the binding sites of proteins is an effective means for predicting protein functions based on their structure information. Despite the importance of this problem and much research in the past, it is still very challenging to predict the binding ligands from the atomic structures of protein binding sites. Here, we designed a new algorithm, TIPSA (Triangulation-based Iterative-closest-point for Protein Surface Alignment), based on the iterative closest point (ICP) algorithm. TIPSA aims to find the maximum number of atoms that can be superposed between two protein binding sites, where any pair of superposed atoms has a distance smaller than a given threshold. The search starts from similar tetrahedra between two binding sites obtained from 3D Delaunay triangulation and uses the Hungarian algorithm to find additional matched atoms. We found that, due to the plasticity of protein binding sites, matching the rigid body of point clouds of protein binding sites is not adequate for satisfactory binding ligand prediction. We further incorporated global geometric information, the radius of gyration of binding site atoms, and used nearest neighbor classification for binding site prediction. Tested on benchmark data, our method achieved a performance comparable to the best methods in the literature, while simultaneously providing the common atom set and atom correspondences.