This paper addresses the issues of semantic representation of composite services and the relationships among the atomic services used to build the composite service, which have not been addressed sufficiently in current service description frameworks. Clear semantics and relationships among internal atomic services can enhance a composite service?s reusability and comprehensibility. In this paper conceptual graph is used to address the issues. A composite service can be represented by merging atomic services? conceptual graphs into a larger and more specialized conceptual graph. The semantics and relations of this composite service can be clearly represented in the graph. Service requirements can be converted into conceptual graph too, and thus graph matching methods could be used to search for required services.