A capacity control valve (1; 2) for controlling a flow rate or pressure of a variable capacity compressor according to a valve opening of a valve section, the capacity control valve comprising: a solenoid (30; 50) including a first plunger (34; 44) having a first rod, and a second plunger (35; 45) having a second rod; a valve main body having a first communication passage through which a fluid at a first pressure (Ps) passes, a second communication passage which is arranged adjacent to the first communication passage and through which a fluid at a second pressure (Pd) passes, a third communication passage through which a fluid at a third pressure (Pc) passes, and a main valve seat arranged in a valve hole for communicating the second communication passage and the third communication passage, wherein the first pressure (Ps) is a suction pressure (Ps) of the variable capacity compressor, the second pressure (Pd) is a discharge pressure (Pd) of the variable capacity compressor, and the third pressure (Pc) is a pressure (Pc) of a crank chamber of the variable capacity compressor; a pressure-sensitive body which is arranged in the valve main body on the third communication passage side and which is configured to extend and contract under an action of a vacuum or air present in its interior space, the suction pressure (Ps), and a force exerted by the second rod on a flange part of the pressure-sensitive body; and a valve body having an intermediate communication passage for communicating the first communication passage and the third communication passage, a main valve part for opening and closing the valve hole by separating from and contacting the main valve seat, and an auxiliary valve part arranged in the intermediate communication passage; wherein the second rod is arranged to penetrate the first plunger (34; 44), the first rod and the valve body and is arranged in the intermediate communication passage, and the first rod is configured to open and close the main valve part and the second rod is configured to open and close the auxiliary valve part. a solenoid (30; 50) including a first plunger (34; 44) having a first rod, and a second plunger (35; 45) having a second rod; a valve main body having a first communication passage through which a fluid at a first pressure (Ps) passes, a second communication passage which is arranged adjacent to the first communication passage and through which a fluid at a second pressure (Pd) passes, a third communication passage through which a fluid at a third pressure (Pc) passes, and a main valve seat arranged in a valve hole for communicating the second communication passage and the third communication passage, wherein the first pressure (Ps) is a suction pressure (Ps) of the variable capacity compressor, the second pressure (Pd) is a discharge pressure (Pd) of the variable capacity compressor, and the third pressure (Pc) is a pressure (Pc) of a crank chamber of the variable capacity compressor; a pressure-sensitive body which is arranged in the valve main body on the third communication passage side and which is configured to extend and contract under an action of a vacuum or air present in its interior space, the suction pressure (Ps), and a force exerted by the second rod on a flange part of the pressure-sensitive body; and a valve body having an intermediate communication passage for communicating the first communication passage and the third communication passage, a main valve part for opening and closing the valve hole by separating from and contacting the main valve seat, and an auxiliary valve part arranged in the intermediate communication passage; wherein the second rod is arranged to penetrate the first plunger (34; 44), the first rod and the valve body and is arranged in the intermediate communication passage, and the first rod is configured to open and close the main valve part and the second rod is configured to open and close the auxiliary valve part.