PURPOSE: In grinding device effecting the grinding of stepped shaft, and feed of rotating stone up to the designated distance frow stepped surface of the stepped shaft, is done in rapid feed and after that it is done in pitch feed. By doing so, feed operation can be done without damaging rotating grinding stone.

CONSTITUTION: When a stepped shaft 1 is fixed to the designated position and a cylinder 12 for a rapid feed device 9 is actuated by positioning a rotating grinding stone 2 in the sufficiently distant place from a stepped surface 1a, a rotating shaft 4 is rotated by means of gearing of a rack 14 and a pinion 15. Then, the rotating grinding stone 2 is fed to the above stepped suface 1a through a rotation and straight movement coverting device 5. After that when the grinding stone 2 reaches to the position spaced by a constant distance l from the stepped surface 1a, the drive of above cylinder 12 stops by a detector 12 and at the same time a cylinder device 25 for a pitch feed device 10 makes a reciprocating movement. Then, a ratchet 20 effects the pitch feed by a claw 29 and the grinding stone 2 effects subsequently the pitch feed.