PURPOSE: To finish a head of a rail, by moving a grinding mechanism which is constituted with a grinding roll and a guide roll along a circular arc provided in an astride manner above the rail.

CONSTITUTION: A frame (a) is mounted on a rail 20 so as to place the center part of a grinding roll 1 on the center part of welding of the rail 20. The rail 20 is pressed from the bottom by turning a handle 90 for clamping and pulling up a claw 103 for clamping. A bolt 66 is turned and the grinding roll 1 is touched the welding part of the rail 20. Circular arc motion is made along a guide rail 70 and the grinding roll 1 is moved after the model of a head of the rail by turning the grinding roll 1 through driving by a motor 21 and turning a handle 80 for a feed roller. With this, processing accuracy is improved, dispersion of character of a finish grinding surface is reduced and a work environment is improved, too.