Ontology matching is an important task to achieve interoperation between semantic web applications using different ontologies. Structural similarity plays a central role in ontology matching. However, the existing approaches rely heavily on lexical similarity, and they mix up lexical similarity with structural similarity. In this paper, we present a graph matching approach for ontologies, called GMO. It uses bipartite graphs to represent ontologies, and measures the structural similarity between graphs by a new measurement. Furthermore, GMO can take a set of matched pairs, which are typically previously found by other approaches, as external input in matching process. Our implementation and experimental results are given to demonstrate the eec tiveness of the graph matching approach.