PURPOSE: To obviate grinding vibration generated in grinding with a simple construction by compounding a vibration attenuating material having creep-like physical property and a grinding wheel base plate so that a grinding wheel itself is provided with self-vibration absorbing property.

CONSTITUTION: This grinding wheel 1 is formed by bonding or applying a vibration attenuating material 3 to the end face of a grinding wheel 2 used for surface grinding, cylinder grinding, internal grinding, centerless grinding and cutting grinding. When the surface grinding is carried out by the thus formed grinding wheel 1, the grinding wheel 2 and the vibration attenuating material 3 are sandwiched by the head 4 of grinding wheel spindle and a flange 5, fastened and mounted by tightening a fastening nut 6 to grind a work piece 7.