To improve measuring accuracy of oxygen storage capacity by excluding deterioration influence of a sensor behind catalyst.

Active air-fuel ratio control for switching an air-fuel ratio on the upstream side of a catalyst between rich/lean is executed in response to overturn of output Vr of the sensor behind catalyst which detects an air-fuel ratio on the downstream side of the catalyst. The oxygen storage capacity of the catalyst is measured in every overturn period of the output Vr of the sensor behind catalyst. The oxygen storage capacity is measured during periods t11 to t12 in which the output Vr of the sensor behind catalyst is normal in the overturn periods. The overturn periods of the output of the sensor behind catalyst are excluded from the measurement periods to exclude the deterioration influence of the sensor behind catalyst.