The invention is a catalyst formed by covering each surface of particles in a ceramic support with an alumina thin film and holding an active catalyst component with the surface of the thin film, which is large in the pore size and porosity and small in the pressure loss irrespectively of forming the alumina thin film on the surface and is produced, for example, by immersing the ceramic support in an aluminum-containing metallic compound, preliminarily firing, immersing in hot water, drying, firing and finally holding the active catalyst component on the alumina thin film on the surface of the support.