PURPOSE: To accurately set a cutting edge position of a long cutting tool by edging the blade and superfinishing front and rear sides of the cutting edge with reference to the cutting edge position in automatic grinding of the cutting edge.

CONSTITUTION: A grinding wheel 11 reduces further its rotational frequency and stops while the contact point between the grinding wheel and the cutting edge 3a of a long cutting tool 3 thinned extremely with an acute angle is pushed to be deflected by a pushing force produced between the grinding wheel and the cutting edge 3a of the long cutting tool 3. When the grinding wheel 11 is then moved gradually to separate from the cutting edge 3a, the deflection of the cutting edge 3a of the long cutting tool 3 returns again to the original state by elasticity and a cutting edge position as the true cutting edge 3a position is set on the lower surface of the grinding wheel 11 in an instant of starting the rotation of the grinding wheel 11. The automatic grinding of the cutting edge 3a is subsequently carried out with reference to the cutting edge position. Also, the cutting edge position in the grinding process by superfinishing grinding wheels 23, 24 is set similarly.