A laminating a plurality of permanent magnets embedded in storage pores, characterized in that each permanent magnet is inserted in each of said storage pore so as to form gaps at the both ends of the storage pore of the field core, thereby to form air paths for cooling air and a mechanism for cooling such a rotor having permanent magnets characterized by forming air paths for cooling air by providing gaps between each of the inner surface of the end plate and the outer surface of the field core, and also forming air paths for cooling air by placing air paths in the axis direction in contact with each of the permanent magnets on both ends of the permanent magnet, and placing an inlet and an outlet of the cooling air on each of said air paths in such a manner that the cooling air enters one end plate and exits the other end plate via each of said air paths are disclosed.