A target air volume for attaining a torque demand is back-calculated from the torque demand by using a parameter that contributes to the efficiency for converting air volume into torque. The parameter value begins to change to decrease the conversion efficiency in response to the torque demand dropping to a second reference value or below and then gradually changes to decrease the conversion efficiency to conform to a further decrease in the torque demand moving from the second reference value toward a first reference value. Here, the first reference value is calculated from the speed of the internal combustion engine, and the second reference value is calculated from an air volume that can attain the first reference value under a second air-fuel ratio and a first air-fuel ratio. While the torque demand is greater than the first reference value, the target air-fuel ratio is set to the first air-fuel ratio. In addition, the target air-fuel ratio is switched from the first air-fuel ratio to a second air-fuel ratio in response to the torque demand being decreased to the first reference value or lower.