The degree of a deterioration in catalyst is determined when the following requirements are satisfied: the operating state of an internal combustion engine (E) is in a predetermined operating state; and the temperature (T1m) of an exhaust gas, which flows into a catalyst (12), is in a second temperature range (ΔT80) in which the upper limit of the second temperature range (ΔT80) is 10% below the upper limit of a first temperature range (ΔT100) between the activation start temperature (Ta) and the activation end temperature (Tb) of the catalyst (12) before a deterioration and the lower limit of the second temperature range (ΔT80) is 10% above the lower limit of the first temperature range (ΔT100). A deterioration index temperature (Tic) is regarded as a shift level of light-off characteristics of the catalyst (12) toward the higher temperature side, and the deterioration index temperature (Tic) is added to the reference determination temperature (T0b) before the deterioration, and the sum is used as the determination temperature (T0) for exhaust gas temperature raising control. According to the above constitution, the degree of deterioration of the catalyst (12) can be estimated without using a concentration sensor for an exhaust gas component such as an NOx concentration sensor with high accuracy, and the worsening of the state of the exhaust gas is suppressed while minimizing the worsening of the fuel consumption.