A piston pump is described for pumping a fluid. The pump includes at least one cylinder having a piston movable inside the cylinder along the longitudinal axis of the cylinder by a drive, each cylinder having at an end face a mounting flange having at least one cylinder opening, and a chamber having a volume that changes when the associated piston is moved in the cylinder. The piston pump has an inlet port for supplying and an outlet port for draining the fluid. A rotatable valve plate is arranged on the other side of the mounting flange. The mounting flange has at least one passage in the region of the inlet port and the outlet port, respectively, through which the fluid can flow between the inlet port and/or the outlet port and the other side of the mounting flange. The valve plate has fluid-transporting means by which, upon rotation of the valve plate at least one cylinder opening can be connected to a passage of the inlet and/or the outlet port.