PURPOSE: To provide an abrasive machine which is able to keep an amount of stock removal of a workpiece such as a round bar and a long pipe or the like constant, reduce the variations in an abrasive state on an outer surface and control the peripheral speed of a grindstone constant.

CONSTITUTION: This abrasive machine is provided with a grindstone 3 grinding a workpiece as rotating in the circumferential direction and a support base 4 supporting this grindstone 3 and traveling in a direction where the grindstone 3 comes close to or separates from the workpiece 2, and in this constitution, installing a distance measuring means 7 measuring a distance up to the outer circumferential surface in the vertical upper part of a position different from a contact position of the workpiece 2 on an outer circumferential surface of the grindstone 3, and also a support base traveling means 8 seeking a variation in the distance to the support base 4 on the basis of an output out of the distance measuring means 7 and shifting the support base 4 as far as the variation in a direction where the grindstone 3 comes close to the workpiece 2, respectively. In addition, a speed control means 9 controlling a peripheral speed of the grindstone 3 constant on the basis of the variation, is installed in the grindstone 3.