Combustion of a trace amount of CH4 over Pd catalysts supported on calcined ZrO2 was examined under nearly exhaust gas conditions where the temperature is not so high and water vapor coexists. High catalytic activity was obtained with ZrO2 support calcined at 1073 and 1273 K. The durability test at 673 K for 100 h revealed that the activity of these catalysts hardly decreased, while that of the Pd catalysts supported on calcined Al2O3 were much decreased in the course of time. These results demonstrated the advantages of ZrO2 as a support for Pd catalysts in the present reaction.