A method for manufacturing a nut for a ball screw, the ball screw comprising: the nut having an inner circumferential surface on which a spiral groove is formed; a threaded shaft having an outer circumferential surface on which a spiral groove is formed; balls loaded in a raceway between the spiral groove of the nut and that of the threaded shaft; and a ball return passage arranged as a letter S shape concave (15, 16; 115, 116) on the inner circumferential surface of the nut for returning the balls from an end point of the raceway to a start point of the raceway, the balls being rolling in the raceway to make the nut relatively move with respect to the threaded shaft, wherein the concave (15, 16; 115, 116) is formed on the inner circumferential surface of the nut blank (1; 101) by plastic working in a pressing method by use of a cam mechanism, the cam mechanism comprising: a cam driver (4, 6; 104; 106) inserted into a cylindrical nut blank (1; 101) and moving in an axial direction of the nut blank (1; 101) at the time of processing; and a cam slider (3, 103A, 103B; 107, 108) disposed between the nut blank (1; 101) and the cam driver (4, 6; 104; 106) and provided with a convex (135, 136; 173, 183) corresponding to the concave (15, 16; 115, 116), a movement of the cam driver (4, 6; 104; 106) causing the convex (135, 136; 173, 183) to move in a radial direction of the nut, wherein a plurality of the concaves (15, 16; 115, 116) are formed on the inner circumferential surface of the nut by a corresponding plurality of the convexes (135, 136; 173, 183) provided on a plurality of the cam sliders (3; 103A, 103B; 107, 108), characterized in that the plurality of the concaves (15, 16; 115, 116) are formed in a uniform manner by changing a movement amount of the plurality of the convexes (135, 136; 173, 183), wherein a movement amount of the plurality of the convexes (135, 136; 173, 183) provided on the plurality of the cam sliders (3; 103A, 103B; 107, 108), moving outwardly in the radial direction of the nut blank (1; 101) are changed by employing convexes having different protruding dimensions in the radial direction or by employing inclined surfaces, where the cam driver (4, 6; 104; 106) is in contact with the cam sliders (3; 103A, 103B; 107, 108), having different angles of inclination. wherein the concave (15, 16; 115, 116) is formed on the inner circumferential surface of the nut blank (1; 101) by plastic working in a pressing method by use of a cam mechanism, the cam mechanism comprising: a cam driver (4, 6; 104; 106) inserted into a cylindrical nut blank (1; 101) and moving in an axial direction of the nut blank (1; 101) at the time of processing; and a cam slider (3, 103A, 103B; 107, 108) disposed between the nut blank (1; 101) and the cam driver (4, 6; 104; 106) and provided with a convex (135, 136; 173, 183) corresponding to the concave (15, 16; 115, 116), a movement of the cam driver (4, 6; 104; 106) causing the convex (135, 136; 173, 183) to move in a radial direction of the nut, wherein a plurality of the concaves (15, 16; 115, 116) are formed on the inner circumferential surface of the nut by a corresponding plurality of the convexes (135, 136; 173, 183) provided on a plurality of the cam sliders (3; 103A, 103B; 107, 108), characterized in that the plurality of the concaves (15, 16; 115, 116) are formed in a uniform manner by changing a movement amount of the plurality of the convexes (135, 136; 173, 183), wherein a movement amount of the plurality of the convexes (135, 136; 173, 183) provided on the plurality of the cam sliders (3; 103A, 103B; 107, 108), moving outwardly in the radial direction of the nut blank (1; 101) are changed by employing convexes having different protruding dimensions in the radial direction or by employing inclined surfaces, where the cam driver (4, 6; 104; 106) is in contact with the cam sliders (3; 103A, 103B; 107, 108), having different angles of inclination.