A vane air motor comprising: a housing having a rotor accommodating chamber with a circular cylindrical inner peripheral surface; a rotor retained in the rotor accommodating chamber rotatably about a rotational center axis parallel to a center axis of the inner peripheral surface, the rotor having a vane accommodating groove defined by an elongated opening formed on an outer peripheral surface of the rotor to extend parallel to the rotational center axis, the vane accommodating groove being further defined by a front side surface and a rear side surface which extend radially inward from a front edge and a rear edge, respectively, of the opening, as viewed in a rotational direction of the rotor, and a bottom surface extending between the front side surface and the rear side surface at a position spaced radially inward from the outer peripheral surface of the rotor; and a vane slidably disposed in the vane accommodating groove; wherein compressed air is supplied from an air supply port opening on the inner peripheral surface and passed around the rotor in one direction before being discharged from an air discharge port located at a position circumferentially spaced from the air supply port, so that the compressed air acts on the vane to rotationally drive the rotor; wherein the air supply port is provided at a central position of the inner peripheral surface in a direction of the center axis; the rotor having cut-out portions for promoting vane pushing-out action which are provided on the outer peripheral surface to intersect the vane accommodating groove at a position spaced from the bottom surface of the vane accommodating groove, characterised by the cut-out portions being defined by cut-out surfaces extending rearward in the rotational direction from the rear side surface of the vane accommodating groove to intersect the outer peripheral surface at opposite ends, respectively, of the vane accommodating groove of the rotor in the direction of the rotational center axis, the cut-out portions for promoting vane pushing-out action provided only at a rear side of the vane accommodating groove. a housing having a rotor accommodating chamber with a circular cylindrical inner peripheral surface; a rotor retained in the rotor accommodating chamber rotatably about a rotational center axis parallel to a center axis of the inner peripheral surface, the rotor having a vane accommodating groove defined by an elongated opening formed on an outer peripheral surface of the rotor to extend parallel to the rotational center axis, the vane accommodating groove being further defined by a front side surface and a rear side surface which extend radially inward from a front edge and a rear edge, respectively, of the opening, as viewed in a rotational direction of the rotor, and a bottom surface extending between the front side surface and the rear side surface at a position spaced radially inward from the outer peripheral surface of the rotor; and a vane slidably disposed in the vane accommodating groove; wherein compressed air is supplied from an air supply port opening on the inner peripheral surface and passed around the rotor in one direction before being discharged from an air discharge port located at a position circumferentially spaced from the air supply port, so that the compressed air acts on the vane to rotationally drive the rotor; wherein the air supply port is provided at a central position of the inner peripheral surface in a direction of the center axis; the rotor having cut-out portions for promoting vane pushing-out action which are provided on the outer peripheral surface to intersect the vane accommodating groove at a position spaced from the bottom surface of the vane accommodating groove,