The output from an air-fuel ratio sensor is corrected using an integral term that is calculated by integrating values of deviation of the output from an oxygen sensor with respect to a reference output that would be obtained when the combustion air-fuel ratio is stoichiometric, when an engine operates with a target combustion air-fuel ratio set to the stoichiometric air-fuel ratio. A fuel-cutoff prohibition period in which fuel supply cutoff is prohibited is set so that the engine continues to operate with the target combustion air-fuel ratio set to the stoichiometric air-fuel ratio, until the integral term is updated at least once. The integral term may be updated when a predetermined updating condition is satisfied.