Abstract: An apparatus for grinding edges of running metal strips by a rotating grinding wheel, including a grinding wheel supporting table carrying thereon the grinding wheel and a motor for driving the grinding wheel, and driving means for forward and backward driving the table toward and away from the edges of the metal strips. According to the invention, the apparatus further comprises a spring arranged between the table and the driving means, springs hanging the table from a stationary member, and control means for controlling the driving means in response to vibration component free signals without being annoyed with variation in load current of the motor for driving the grinding wheel, thereby eliminating the uneven grinding due to external disturbance during the running of the metal strip.