A manufacture method for a metal-supported catalyst in accordance with an embodiment of the invention includes: binding a compound having a coordinatable functional group onto a catalyst support; impregnating the catalyst support to which the compound having the coordinatable functional group is bound, with a solution that contains a metal complex in which a ligand is coordinated to one catalyst metal atom or a plurality of catalyst metal atoms of the same kind, and substituting at least partially the ligand coordinated in the metal complex with the coordinatable functional group of the compound bound to the metal oxide support; and drying and firing the catalyst support impregnated with the solution.