Ontology matching is defined as finding a relationship or correspondence between two or more entities in two or more ontologies. To solve the interoperability problem of the domain ontologies, semantically similar entities in these ontologies must be found and aligned before merging them. GraphMatcher, developed in this study, is an ontology matching system using a graph attention approach to compute higher-level representation of a class together with its surrounding terms. The GraphMatcher has obtained remarkable results in in the Ontology Alignment Evaluation Initiative (OAEI) 2022 conference track. Its codes are available at ~\url{https://github.com/sefeoglu/gat_ontology_matching}.