A target air amount for achieving a requested torque is back-calculated from the requested torque using a parameter that provides a conversion efficiency of an air amount to torque. The value of the parameter gradually changes to lower the conversion efficiency as the requested torque decreases from a second reference value towards a first reference value. The first reference value is calculated based on the engine speed. The second reference value is calculated based on an air amount with which the first reference value is achieved under a second air-fuel ratio, and a first air-fuel ratio. The target air-fuel ratio is set to the first air-fuel ratio when the requested torque is greater than the first reference value, and is switched from the first air-fuel ratio to the second air-fuel ratio when the requested torque decreases to a value equal to or less than the first reference value.