A hydraulic piston pump in which a cylinder port (4b) can be communicated with a discharge port (9) after a system pressure (Po) and a chamber pressure (Pi) in a cylinder bore are in an equilibrium state. A through-hole (16) opened in that surface of a valve plate (7) on which a cylinder block (3) slides is communicated with one end surface (21a) side of a balance valve (20), and the system pressure (Po) on the discharge port (9) side is supplied to the other end surface (21b) of the balance valve. A balance piston (21) is built-in in the balance valve, and the balance piston (21) slides by a pressure difference between the chamber pressure (Pi) in the cylinder bore (4) and the system pressure (Po). Before a cylinder port (4b) is communicated with an oil guiding groove (15), the chamber pressure (Pi) and the system pressure (Po) can be brought into an equilibrium state by actuation of the balance piston (21).