Chemical-protein interaction (CPI) is the central topic of target identification and drug discovery. However, large scale determination of CPI is a big challenge for in vitro or in vivo experiments, while in silico prediction shows great advantages due to low cost and high accuracy. On the basis of our previous drug-target interaction prediction via network-based inference (NBI) method, we further developed node- and edge-weighted NBI methods for CPI prediction here. Two comprehensive CPI bipartite networks extracted from ChEMBL database were used to evaluate the methods, one containing 17,111 CPI pairs between 4,741 compounds and 97 G protein-coupled receptors, the other including 13,648 CPI pairs between 2,827 compounds and 206 kinases. The range of the area under receiver operating characteristic curves was 0.73 to 0.83 for the external validation sets, which confirmed the reliability of the prediction. The weak-interaction hypothesis in CPI network was identified by the edge-weighted NBI method. Moreover, to validate the methods, several candidate targets were predicted for five approved drugs, namely imatinib, dasatinib, sertindole, olanzapine and ziprasidone. The molecular hypotheses and experimental evidence for these predictions were further provided. These results confirmed that our methods have potential values in understanding molecular basis of drug polypharmacology and would be helpful for drug repositioning.