To effectively grind a sheave surface 101b formed of a curved and tapered peripheral surface with high quality.

When grinding a sheave member 101, the sheave member 101 provided with the sheave surface 101b forming the curved and tapered peripheral surface is fed and rotated around a first axis Z, a grinding wheel 19 is rotated around a rotating central axis 20 of the grinding wheel positioned on a plane containing the first axis Z, and a grinding peripheral surface 19a is brought into contact with the sheave surface 101b. The grinding peripheral surface 19a is made a straight cylindrical face in parallel with the rotating central axis 20 of the grinding wheel, and a diametral surface 19b of the grinding wheel 19 is constantly vertically faced to each place to be ground of the sheave surface 101b by using a numerical control device 25 when the grinding peripheral surface 19a is brought into contact with each place to be ground of the sheave surface 101b.