An air compressor includes an internal combustion engine for driving an air compressing part that generates compressed air, which is stored in an air-storage tank. At a point in time when the air pressure inside the air-storage tank has increased to a first set pressure, the supply of fuel to the engine is cut off, thereby stopping the engine and the combustion of fuel. At a point in time when the air pressure inside the air-storage tank has decreased from the first set pressure to a second set pressure, a starter motor is started up to resume the operation of the engine.