Recent studies concerning thermal stabilization of catalyst supports and their application to a catalytic gas turbine combustor were reviewed. Development of heat-resistant catalysts has received considerable attention for the development of high-temperature combustion catalysts. The use of additives such as La, Si, Ba, etc., is a promising way to improve the thermal stability of alumina-based support materials. Preparation routes also influence the surface area and the pore structure at operation temperatures. The effects were discussed from the solid state sintering mechanism of transition alumina. The authors have developed a noble alumina-based catalyst, hexaaluminate, as a thermally stable combustion catalyst, which can be used above 1200 degrees C. In the second half of this review, we discussed fundamental catalytic properties of hexaaluminates and the results of practical applications to a gas turbine combustor.