A compressor has a cam plate located in a crank chamber and mounted on a drive shaft and a piston coupled to the cam plate and located in a cylinder bore. The piston compresses gas supplied to the cylinder bore from a separate external circuit by way of a suction chamber and discharges the compressed gas to the external circuit by way of a discharge chamber. The cam plate is tiltable between a maximum inclined angle position and a minimum inclined angle position with respect to a plane perpendicular to an axis of the drive shaft according to a difference between the pressure in the crank chamber and the pressure in the cylinder bore. The piston moves by the stroke based on an inclination of the cam plate to control the displacement of the compressor. A valve is placed between the discharge chamber and the external circuit. The valve selectively connects and disconnects the discharge chamber with the external circuit based on a difference between the pressure acting on the upstream side of the valve and the pressure acting on the downstream side of the valve.