Drug discovery is important in cancer therapy and precision medicines. Traditional approaches of drug discovery are mainly based on in vivo animal experiments and in vitro drug screening, but these methods are usually expensive and laborious. In the last decade, omics data explosion provides an opportunity for computational prediction of anti-cancer drugs, improving the efficiency of drug discovery. High-throughput transcriptome data were widely used in biomarkers' identification and drug prediction by integrating with drug-response data. Moreover, biological network theory and methodology were also successfully applied to the anti-cancer drug discovery, such as studies based on protein-protein interaction network, drug-target network and disease-gene network. In this review, we summarized and discussed the bioinformatics approaches for predicting anti-cancer drugs and drug combinations based on the multi-omic data, including transcriptomics, toxicogenomics, functional genomics and biological network. We believe that the general overview of available databases and current computational methods will be helpful for the development of novel cancer therapy strategies.