This paper presents a computational approach designed to construct and query a literature-based knowledge graph for predicting novel drug therapeutics. The main objective is to offer a platform that discovers drug combinations from FDA-approved drugs and accelerates their investigations by domain scientists. Specifically, the paper introduced the following algorithms: (1) an algorithm for constructing the knowledge graph from drug, gene, and disease mentions in the biomedical literature; (2) an algorithm for vetting the knowledge graph from drug combinations that may pose a risk of drug interaction; (3) and two querying algorithms for searching the knowledge graph by a single drug or a combination of drugs. The resulting knowledge graph had 844 drugs, 306 gene/protein features, and 19 disease mentions. The original number of drug combinations generated was 2,001. We queried the knowledge graph to eliminate noise generated from chemicals that are not drugs. This step resulted in 614 drug combinations. When vetting the knowledge graph to eliminate the potentially risky drug combinations, it resulted in predicting 200 combinations. Our domain expert manually eliminated extra 54 combinations which left only 146 combination candidates. Our three-layered knowledge graph, empowered by our algorithms, offered a tool that predicted drug combination therapeutics for scientists who can further investigate from the viewpoint of drug targets and side effects.