One particular challenge in biomedical named entity recognition (NER) and normalization is the identification and resolution of composite named entities, where a single span refers to more than one concept (e.g., BRCA1/2). Previous NER and normalization studies have either ignored composite mentions, used simple ad hoc rules, or only handled coordination ellipsis, making a robust approach for handling multitype composite mentions greatly needed. To this end, we propose a hybrid method integrating a machine-learning model with a pattern identification strategy to identify the individual components of each composite mention. Our method, which we have named SimConcept, is the first to systematically handle many types of composite mentions. The technique achieves high performance in identifying and resolving composite mentions for three key biological entities: genes (90.42% in F-measure), diseases (86.47% in F-measure), and chemicals (86.05% in F-measure). Furthermore, our results show that using our SimConcept method can subsequently improve the performance of gene and disease concept recognition and normalization. SimConcept is available for download at: http://www.ncbi.nlm.nih.gov/CBBresearch/Lu/Demo/SimConcept/.