A catalyst for oxidation of hydrogen, which is characterized in that: A. it is a catalyst having platinum supported on alumina; B. said alumina has a BET specific surface area of from 0.5 to 6 m.sup.2 /g; and C. said alumina has an ammonia adsorption of at most 5 .mu.mol/g, is used at the time of producing an unsaturated hydrocarbon by dehydrogenation of a hydrocarbon, whereby hydrogen present in the gas mixture can selectively be oxidized, and thus, the yield can be improved particularly when styrene is produced by dehydrogenation of ethylbenzene.