The vane pump has a housing containing a rotor driven by a drive shaft. A number of grooves are distributed over the rotor circumference and extend in a substantially radial direction of the rotor, in each of which grooves a wing-shaped delivery element is guided in sliding fashion. The rotor is surrounded by a circumferential wall that extends eccentrically in relation to its rotation axis against which the radially outer ends of the delivery elements rest. Housing end walls of the pump housing adjoin the rotor in the direction of its rotation axis. An annular groove encompassing the rotation axis of the rotor is provided in at least one of the housing end walls and is situated opposite the radially inner regions of the grooves of the rotor and communicates with the pressure region via a connecting groove in the housing end wall. The connecting groove extends from the pressure region radially inward in the rotation direction of the rotor to the annular groove.