An air supply apparatus supplies atmospheric air to an external apparatus such as an air demander. The air supply apparatus comprises a pump, an actuator, a power consumption detector, an air pressure detector, and a controller. The pump takes in atmospheric air and discharges the atmospheric air to the external apparatus. The actuator actuates the pump. The power consumption detector detects a measurement value corresponding to a power consumption of the actuator. The air pressure detector detects a discharge pressure of the atmospheric air discharged by the pump. The controller calculates a criterion value of the measurement value when the pump takes in the atmospheric air at 1 atmospheric pressure and discharges the atmospheric air at the discharge pressure based on the rotational frequency of the pump and the measurement value. The controller also adjusts the rotational frequency based on the measurement value and the criterion value.