A major challenge in the field of protein-protein docking is to discriminate between the many wrong and few near-native conformations, i.e. scoring. Here, we introduce combinatorial complex-type-dependent scoring functions for different types of protein-protein complexes, protease/inhibitor, antibody/antigen, enzyme/inhibitor and others. The scoring functions incorporate both physical and knowledge-based potentials, i.e. atomic contact energy (ACE), the residue pair potential (RP), electrostatic and van der Waals' interactions. For different type complexes, the weights of the scoring functions were optimized by the multiple linear regression method, in which only top 300 structures with ligand root mean square deviation (L_RMSD) less than 20 A from the bound (co-crystallized) docking of 57 complexes were used to construct a training set. We employed the bound docking studies to examine the quality of the scoring function, and also extend to the unbound (separately crystallized) docking studies and extra 8 protein-protein complexes. In bound docking of the 57 cases, the first hits of protease/inhibitor cases are all ranked in the top 5. For the cases of antibody/antigen, enzyme/inhibitor and others, there are 17/19, 5/6 and 13/15 cases with the first hits ranked in the top 10, respectively. In unbound docking studies, the first hits of 9/17 protease/inhibitor, 6/19 antibody/antigen, 1/6 enzyme/inhibitor and 6/15 others' complexes are ranked in the top 10. Additionally, for the extra 8 cases, the first hits of the two protease/inhibitor cases are ranked in the top for the bound and unbound test. For the two enzyme/inhibitor cases, the first hits are ranked 1st for bound test, and the 119th and 17th for the unbound test. For the others, the ranks of the first hits are the 1st for the bound test and the 12th for the 1WQ1 unbound test. To some extent, the results validated our divide-and-conquer strategy in the docking study, which might hopefully shed light on the prediction of protein-protein interactions.