A vane pump for an automatic transmission includes a housing which may be spaced from the axis of the transmission input shaft axis and driven by a chain or gear train driven by the torque converter hub or disposed on and about the axis of the transmission input shaft and driven at engine speed. The vane pump includes a pair of port plates which reside on the end faces of a pump body having a cylindrical chamber which receives an eccentrically disposed rotor that is coupled to a stub shaft in an off-axis arrangement. The rotor includes a plurality of radial slots which receive a like plurality of vanes. The outer ends or edges of the vanes are in contact with the wall of the cylindrical chamber and the inner ends or edges are in contact with a pair of vane rings received within recesses in the ends of the rotor. The vanes are thus constrained between the wall of the chamber and the vane rings which positively determine their radial positions as they and the rotor rotate. Suitable inlet (suction) and outlet (pressure) ports in the port plates supply and collect hydraulic fluid to and from the cylindrical chamber. A compression spring biases the port plates and body together. The vane pump according to the present invention is self-priming and achieves high pumping efficiency.