Over the past decade Structural Genomics projects have accumulated structural data for over 75,000 proteins, but the function of most of them are unknown due to limitation of laboratory approaches for discovering the functionality of proteins. Computational methods play key roles to minimize this gap. Graphs are often used to describe and analyze the geometry and physicochemical composition of bimolecular structures such as, chemical compounds and protein functional sites. In this study, we developed an innovative graph method to represent protein surface based on how amino acid residues contact with each other. Further, we implemented a shortest-path graph kernel method to calculate similarities between the graphs. The nearest-neighbor method was used to compare the similarity of kernel values and predict functional sites of protein structures. The proposed approach achieved accuracy as high as 77.1% and would provide a useful tool for functional site prediction.