A diaphragm air pump comprises a pump chamber, a diaphragm and one or more piezoelectric beams or bimorphs. Fluid flows into the pump chamber and then flows out of it, the diaphragm is provided within the pump chamber, and one or more central openings are formed in the diaphragm. One or more central check valves are provided in the central openings. The diaphragm is just bonded with piezoelectric beams, not fixed to the lower housing of the pump chamber in order to get large displacement. With the provided diaphragm air pump, it is possible to actively adjust the air quantity according to the requirement for fuel cell or a part-to-be-cooled, and it is also possible to reduce noise and power consumption compared with a conventional fan type cooler or air pumps.