The identification of beneficial drug combinations is a challenging issue in pharmaceutical and clinical research toward combinatorial drug therapy. In the present study, we developed a novel computational method for large-scale prediction of beneficial drug combinations using drug efficacy and target profiles. We designed an informative descriptor for each drug-drug pair based on multiple drug profiles representing drug-targeted proteins and Anatomical Therapeutic Chemical Classification System codes. Then, we constructed a predictive model by learning a sparsity-induced classifier based on known drug combinations from the Orange Book and KEGG DRUG databases. Our results show that the proposed method outperforms the previous methods in terms of the accuracy of high-confidence predictions, and the extracted features are biologically meaningful. Finally, we performed a comprehensive prediction of novel drug combinations for 2,639 approved drugs, which predicted 142,988 new potentially beneficial drug-drug pairs. We showed several examples of successfully predicted drug combinations for a variety of diseases.