The NOx catalyst is irradiated with an electromagnetic wave, a resonance frequency and a ratio of a reception power to an oscillation power at the time of the irradiation are detected, and an upper limit value of a change amount of the resonance frequency or an upper limit value of a change amount of the ratio at which the NOx catalyst is diagnosed to be abnormal is determined from a change amount of the resonance frequency and a change amount of the ratio until water is adsorbed on all acid sites included in the NOx catalyst, and a change amount of the resonance frequency and a change amount of the ratio until ammonia is adsorbed on all acid sites included in the NOx catalyst, when it is supposed that the NOx catalyst is in a state of being on the borderline between normal and abnormal.