First shaped item with shaft part is produced by forward extrusion forming of work, and further, upset forming thereof is carried out to thereby obtain second shaped item with large-diameter part. Subsequently, backward extrusion forming of the second shaped item is carried out to thereby obtain third shaped item having not only cup part provided with ball rolling grooves but also circular diameter expansion portion provided at the mouth area of the inside wall of the cup part along the circumferential direction in such a fashion that the diameter is gradually expanded from the bottom side toward the opening side. Outer ring member for constant-velocity joint is obtained by further subjecting the third shaped item to low-temperature annealing treatment, shot blast treatment and lubricating chemical coating treatment, and thereafter to ironing forming.