A claw pump includes: a housing; two rotating shafts which are disposed parallel; a pair of rotors respectively fixed to the two rotating shafts; a rotary drive device driving the pair of rotors; and a suction port and discharge ports formed in a partition wall of the housing. The discharge ports are constituted by a first discharge port and a second discharge port. The first discharge port is formed at a position that communicates with an initial stage compression space formed at an initial stage of a compression stroke in a compression space that is formed by joining a first pocket and a second pocket. The claw pump includes an opening/closing mechanism which opens the first discharge port when a pressure of the initial stage compression space reaches a threshold and closes the first discharge port when the pressure does not reach the threshold.