Protein-protein docking technology is an effective approach to study the molecular mechanism of essential biological processes mediated by complex protein-protein interactions. The fast Fourier transform (FFT) correlation approach makes a good balance between the exhaustive global sampling and the computational efficiency for protein-protein docking. However, it is difficult to integrate the precise knowledge-based scoring function and site constraint information into the FFT-based approach. New docking strategies with the capability of combining both global sampling and precise scoring are strongly needed. We propose a multistage protein-protein docking strategy called CoDockPP. This program takes full advantage of the sampling efficiency of the FFT-based method to choose the valid ligand protein poses with good surface complementarity. The retained poses are transformed to the real Cartesian space for the implementation of site constraints and atomic scoring. Site constraints and a rapid table lookup scoring are applied to gradually reduce the candidate poses to a tractable number. To enhance the accuracy of docking prediction, the best fast-scoring states are expanded the local sampling points and then these neighbor poses are further evaluated by the precise knowledge-based scoring function. By testing on protein-protein docking benchmark 5.0, CoDockPP remarkably improves the success rate and hit count in both ab initio docking and site-specific docking, especially in difficult cases. The server is free and open to all users with no login requirement at http://codockpp.schanglab.org.cn .