A closed-die forging having an annular flat surface portion and a corner portion at an outer periphery of the annular flat surface portion is made by a method consisting of a rough forging process and a finish forging process. In the rough forging process, a rough forged product is shaped so as to have an annular flat surface portion smaller in outer diameter than the first mentioned annular flat surface portion and a conical surface portion at an outer periphery of the second mentioned annular flat surface portion. The conical surface portion is so shaped as to extend increasingly outwards as it extend in the same direction of movement of a punch of a rough forging die for performing a forming operation. In the finish forging process, the conical surface portion is pushed by a punch of a finish forging die in the same direction as the rough forging product is pushed by the first mentioned punch in the rough forging process and thereby formed together with the second mentioned annular flat surface into the first mentioned annular flat surface portion perpendicular to the direction of movement of the second mentioned punch.