The problem of mining undiscovered public knowledge from biomedical literature was exemplified by Swanson's pioneering work on Raynaud disease/fish-oil discovery in 1986. Since then, there have been many approaches to mine undiscovered public knowledge from biomedical literature. This paper presents a semantic-based approach for mining undiscovered public knowledge from biomedical literature. The method takes advantages of the biomedical ontologies, MeSH and UMLS, as the source of semantic knowledge. A prototype system Biomedical Semantic-based Knowledge Discovery System (Bio-SbKDS) is designed to uncover novel hypothesis/connections hidden in the biomedical literature. Using the semantic types and semantic relations of the biomedical concepts, Bio-SbKDS can identify the relevant concepts collected from Medline and generate the novel hypothesis between these concepts. Bio-SbKDS successfully replicates Dr. Swanson's two famous discoveries: Raynaud disease/fish oil and migraine/magnesium. Compared with previous approaches, our method searches much less articles, generates much less but more relevant novel hypotheses, requires much less human intervention in the discovery procedure.