To suppress degradation of fuel consumption and exhaust emission during deterioration diagnosis of an oxidation catalyst.

An index value for the oxidation catalyst regarding the capability of adsorbing another specified component than hydrocarbon is measured, and the deterioration of the oxidation catalyst is determined in accordance with the measured index value. The specified component is preferably NOx. Preferably, the amount of NOx desorbed from the oxidation catalyst when supplying hydrocarbon to the oxidation catalyst is measured as the index value. A smaller amount of hydrocarbon is required for desorption, therefore suppressing the worsening of fuel consumption and exhaust emission during deterioration diagnosis.