In this paper, we propose an ontology-based conceptual modeling framework for military mission space, which is called the Conceptual Models of the Mission Space-Korea (CMMS-K). By using CMMS-K, we develop conceptual models of military mission space, through which the semantic interoperability and reusability of simulation models are supported. In the military domain, actions and behaviors play a critical role in describing simulation scenarios. This paper presents a task ontology as a component of CMMS-K in order to represent and reuse actions and behaviors more consistently and systematically than previous modeling approaches. Specifically, the proposed task ontology provides a scheme for representing domain knowledge about an action or a task, which is a group of actions. To develop a mission space model comprising actions in the task ontology, we employ the process model of OWL-S, with which the semantic description of Web services is represented. To show the feasibility of the proposed conceptual modeling approach, the paper illustrates a case study on developing a conceptual model for close air support scenarios.