Multidrug regimens are a promising strategy for improving therapeutic efficacy and reducing side effects, especially for complex disorders such as cancer. However, the use of multidrug therapies is very challenging, due to a lack of understanding of the mechanisms of drug interactions. We herein present a novel computational approach-Drug-Induced Genomic Residual Effect (DIGRE) Computational Model-to predict drug combination effects by explicitly modeling drug response curves and gene expression changes after drug treatments. The prediction performance of DIGRE was evaluated using two datasets: (i) OCI-LY3 B-lymphoma cells treated with 14 different drugs and (ii) MCF breast cancer cells treated with combinations of gefitinib and docetaxel at different doses. In both datasets, the predicted drug combination effects significantly correlated with the experimental results. The results indicated the model was useful in predicting drug combination effects, which may greatly facilitate the discovery of new, effective multidrug therapies.