The invention relates to a piston pump for conveying a fluid, in particular in a vehicle brake system. The piston pump has a cylinder and a piston movably disposed in the cylinder. A restoring element preloads the piston, and a drive unit for actuates the piston in the cylinder to pump the fluid into a pressure chamber formed in the cylinder. The piston is embodied by a first piston par and a second piston part. The first piston part is a cylindrical body, which can be moved by the drive unit. The second piston part form the piston base, in which four radial inlet openings and one axial connection opening for communication with the pressure chamber are disposed. A flange for the disposition of a seal is disposed on the outer circumference of the piston base element. The openings are simple to make in the face ends and circumferential regions of the second piston part.