The invention relates to a carrier-supported catalyst comprising oxides of chromium and tungsten and at least one of the oxides of molybdenum and potassium in the atomic ratio of Cr.sub.1 W.sub.0.1-0.5 Mo.sub.0-0.05 K.sub.0-0.5 on a porous carrier material, and to a process for making it. To this end, the process provides(a) for a dry porous carrier material to be saturated with water up to 40 to 80% of its predetermined saturation value;(b) for the carrier material treated as under (a) to be impregnated in any sequential order, but at least once with an aqueous solution of water-soluble compounds of chromium and, if desired, potassium, and sequentially, but at least once with a separately produced aqueous solution of a water-soluble compound of tungsten and, if desired, molybdenum, the aqueous solutions being used in either case in a quantity which is at most necessary for complete saturation;(c) for the carrier material to be dried after each impregnation over a period of 2 to 20 hours at 350 to 500 K, and(d) for the carrier material to be sintered over a period of 0.5 to 12 hours at 550 to 1000 K, in a stream of air.The carrier-supported catalyst finds use in the production of styrene by subjecting ethylbenzene to oxidative dehydrogenation with molecular oxygen in gas phase.