Functional elucidation of uncharacterized protein structures is an important task in bioinformatics. We report our new approach for structure-based function prediction which captures local surface features of ligand binding pockets. Function of proteins, specifically, binding ligands of proteins, can be predicted by finding similar local surface regions of known proteins. To enable partial comparison of binding sites in proteins, a weighted bipartite matching algorithm is used to match pairs of surface patches. The surface patches are encoded with the 3D Zernike descriptors. Unlike the existing methods which compare global characteristics of the protein fold or the global pocket shape, the local surface patch method can find functional similarity between non-homologous proteins and binding pockets for flexible ligand molecules. The proposed method improves prediction results over global pocket shape-based method which was previously developed by our group.