Although biomedical ontologies have been widely used in the life science domain, the heterogeneous problem among biomedical ontologies hampers their inter-operability. Thus, the establishment of meaningful links between heterogeneous biomedical ontologies, so-called biomedical ontology matching, is critical to the success of biomedical ontology engineering. To determine the biomedical ontology alignment with high quality, in this work, a Hybrid Compact Differential Evolution (HCDE) algorithm-based biomedical ontology matching technique is proposed. In particular, we propose a similarity metric on biomedical concepts, construct an optimal model for the biomedical ontology matching problem, and introduce a binomial crossover into CDE's evolving the process to enhance its performance. The experiments are carried out on the Disease and Phenotype track and Biodiversity and Ecology track from the Ontology Alignment Evaluation Initiative (OAEI 2018). The experimental results show that HCDE can significantly improve the CDE in terms of the alignment's quality, and the alignments obtained by HCDE are also better than OAEI 2018's participants.