A compressed air supply apparatus includes a pressure measurement unit which measures air pressure of an air tank connected with an air compressor with a shortest flow path among a plurality of air tanks connected with the air compressor and communicated with one another, and a control unit configured to operate an air compressor when a measurement value of the pressure measurement unit reaches a first pressure or less, and configured to stop the air compressor when the measurement value reaches a second pressure higher than the first pressure, and relief valve apparatuses installed in each of the connection flow path between the air compressor and each of a plurality of air tanks, wherein the relief valve apparatus includes a flow limiting unit which limits flow of air and a valve body arranged closer to the air tank side than the flow limiting unit and configured to open the connection flow path to the atmosphere when the measurement value reaches a third pressure higher than the second pressure and close the connection flow path when the measurement value reaches a fourth pressure higher than the second pressure and lower than the third pressure after the opening.