A turbine electric power generator is provided with winding slots and sub-slots of a rotor; rotor windings having conductors and insulation materials laminated alternately thereon; wedges; and radial ventilation flow passages communicating the sub-slots with through holes of the wedges. In this turbine electric power generator, a projection is provided on an inner face of the radial ventilation flow passages, and the projection height is changed at a rotational axial position. In this manner, there can be provided a gas cooling type rotary electric power generator for turbine with its high cooling performance and high reliability at a low cost.