A total amount of NOX that flows into an NOX catalyst between the time that air-fuel ratio control ends and the time that the air-fuel ratio control starts the next time, is obtained. A total stored amount, which is the sum of an oxygen stored amount and an stored amount in the NOX catalyst before the air-fuel ratio control started, is calculated based on the amount of reducing agent that has flowed into the NOX catalyst during the air-fuel ratio control. The oxygen stored amount is calculated by extrapolating a relationship between the total amount of NOX and the total stored amount. The relationship is established beforehand by executing the air-fuel ratio control with at least two levels.