Density functional theory (DFT) calculations propose that nanometer-sized hydrographene species, graphene-based clusters terminated by H atoms are a promising candidate for a support material for Pt catalysts in fuel cell. The proposal is based on the following three criteria: a small HOMO-LUMO gap of a nanometer-sized hydrographene species with and without a Pt cluster being comparable to zero-gap in infinite-size graphene, strengthening interactions of a Pt cluster with hydrographene species by utilizing its edge, and spontaneous H(2) activation by a Pt cluster on a carbon surface.