Molecular docking is an important method for the research of protein-protein interaction and recognition. A protein can be considered as a network when the residues are treated as its nodes. With the contact energy between residues as link weight, a weighted residue network is constructed in this paper. Two weighted parameters ( strength and weighted average nearest neighbors' degree) are introduced into this model at the same time. The stability of a protein is characterized by its strength. The global topological properties of the protein-protein complex are reflected by the weighted average nearest neighbors' degree. Based on this weighted network model and these two parameters, a new docking scoring function is proposed in this paper. The scoring and ranking for 42 systems' bound and unbounded docking results are performed with this new scoring function. Comparing the results obtained from this new scoring function with that from the pair potentials scoring function, we found that this new scoring function has a similar performance to the pair potentials on some items, and this new scoring function can get a better success rate. The calculation of this new scoring function is easy, and the result of its scoring and ranking is acceptable. This work can help us better understand the mechanisms of protein-protein interactions and recognition.