A vane pump is composed of a casing having a cylindrical inner bore and a rotor disposed in the inner bore with an eccentric relation to the inner bore. A circular pump chamber formed between the rotor and the inner bore is divided by vanes disposed in the rotor into plural pump chambers each changing its capacity according to rotation of the rotor. The vane is slidably disposed in a groove formed in the rotor in a slanted relation with respect to a rotational axis of the rotor. When the rotor rotates, the vane is pushed backward of the rotational direction by fluid in the pump chamber. The pushing force includes a component for pushing the vane upward toward an upper plate closing an upper opening of the inner bore. The vane is pushed against the upper plate to thereby prevent hitting noises between the vane and the upper plate.