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Computational function prediction is one of the most important problems in bioinformatics as elucidating the function of genes is a central task in molecular biology and genomics. Most of the existing function prediction methods use protein sequences as the primary source of input information because the sequence is the most available information for query proteins. There are attempts to consider other attributes of query proteins. Among these attributes, the three-dimensional (3D) structure of proteins is known to be very useful in identifying the evolutionary relationship of proteins, from which functional similarity can be inferred. Here, we report a novel protein function prediction method, ContactPFP, which uses predicted residue-residue contact maps as input structural features of query proteins. Although 3D structure information is known to be useful, it has not been routinely used in function prediction because the 3D structure is not experimentally determined for many proteins. In ContactPFP, we overcome this limitation by using residue-residue contact prediction, which has become increasingly accurate due to rapid development in the protein structure prediction field. ContactPFP takes a query protein sequence as input and uses predicted residue-residue contact as a proxy for the 3D protein structure. To characterize how predicted contacts contribute to function prediction accuracy, we compared the performance of ContactPFP with several well-established sequence-based function prediction methods. The comparative study revealed the advantages and weaknesses of ContactPFP compared to contemporary sequence-based methods. There were many cases where it showed higher prediction accuracy. We examined factors that affected the accuracy of ContactPFP using several illustrative cases that highlight the strength of our method.