PURPOSE: To constantly grind at the most appropriate grinding rate by varying the running speed of a band saw or the grinding power of a grinding belt corresponding to the calculated necessary grinding rate.

CONSTITUTION: When grinding by pressing a grinding belt 7 against a running band steel 2, the surface condition of the band steel 2 is detected to calculate the necessary grinding rate. The necessary grinding rate signal 21 is input to a setting device 31 to output necessary grinding rate signals 23 to each section of the band steel by repeating count-reset of band saw running rate pulse signal 22. The grinding rate signal 23 is input to a speed operator 32 to be compared with a grinding speed setting range singal 24, and when the grinding rate is large within the range, the device operates to slow down the speed of grinding, and the speed of a DC motor 4 is controlled by the speed signal 25 through a control circuit 34 to run the band steel at the speed that counterbalances the necessary grinding rate. On the other hand, the grinding rate signal 23 is input to a current operator 33 to output current signal 28 in proportion to the grinding rate signal 23 to generate grinding power which corresponde to the necessary grinding rate at a motor 8 through a control circuit 35.