A high performance catalyst for combustion having a cheap and heat-resistant carrier capable of retaining a high specific surface area even when it is used at a high temperature of 1,000.degree. C. or higher for a long time, and a process for producing the same are provided, which catalyst comprising a compound expressed by a composition formula of BaAl.sub.12 O.sub.19, and said process comprises kneading .gamma.-alumina or aluminum hydroxide and a barium compound or impregnating the former compound with the latter so as to give an atomic ratio of Al/Ba in the range of 100/1 to 100/15, followed by calcination.