Catalytic combustion of methane has been investigated for the application to gas turbines. As the combustion is operated at high temperatures and high space velocity, heterogeneous reaction and surface initiated gas phase reaction proceed concurrently. Thermal resistance to maintain large surface area is, therefore, requested to attain high combustion efficiency above 1000 degrees C. Hexaaluminate compounds were effective in maintaining large surface area. On the other hand, palladium catalysts were generally employed for the combustion of methane below 1000 degrees C. The prototype catalyst combustors were successfully tested with their high combustion efficiency and low NOx emission by using Pd based- and/or hexaaluminate catalysts.