A method for producing a catalyst having high catalytic activity even at high temperatures of 1200.degree. C. or higher. Fine alumina particles, of which 50% by weight or more have a particle size of 100 nm or less, are mixed with a catalytic component and a substance of inhibiting the sintering of fine alumina particles to form a slurry mixture. This slurry is dried and then calcined to obtain a porous catalyst. The fine alumina particles in the porous catalyst have a large specific surface area even at high temperatures and therefore the porous catalyst maintains its high catalytic activity even at high temperatures of 1200.degree. C. or higher.