To achieve a smooth turning of a rotation plate at a transition period and to make a leakage amount from a space between the rotation plate and a cylinder less at the time of controlling of a predetermined capacity such as the maximum capacity or the minimum capacity in a compressor carrying out a stepwise displacement control.

A rotation plate formed out of a notch is arranged at one end side of a cylinder and a rotation plate pressure chamber for urging this rotation plate to a cylinder side is connected to a discharge pressure side of the compressor through a throttle. The compressor is provided with a switching mechanism for selectively switching and connecting a piston top pressure chamber of a piston of a driving mechanism for rotating the rotation plate to the rotation plate pressure chamber, a suction pressure side of the compressor or the suction pressure side with the rotation plate pressure chamber.