Business process modeling is a critical area of business application as business processes increase in complexity and become more automated. However, little attention has been paid to the fact that business process modelers often misunderstand domain concepts or relationships due to a lack of precise domain knowledge. This semantic ambiguity problem often affects the efficiency and quality of business process modeling. To address this problem, we propose a domain ontology based approach (DOBA) to supporting business process design by capturing domain semantics with a meta model of process ontologies. DOBA provides a means to capture rich, semantic information on complex business processes, which enables the incorporation of domain specific ontologies to facilitate modeling of business processes. The validity of DOBA is demonstrated via a business case in electronic auctions. The DOBA approach represents a first step towards developing a formal methodology for ontology-based modeling and analysis in business process management.