A rotary electric machine for a vehicle has a rotor with a rotor shaft, a pair of rotor cores, a field winding and an annular core made of a stack of core sheets. The rotor core has a boss, a disc portion and a cylindrical part. The cylindrical part is connected with the disc portion and is continuous along the rotor shaft. The cylindrical part is formed with projections and recesses which are disposed alternately in a circumferential direction on the outer periphery thereof. Permanent magnets may be disposed in the recesses. The annular core is connected with outer peripheries of the projections of the cylindrical parts. By adopting the cylindrical parts and the annular core, diameter of the boss is enlarged.