PURPOSE: To improve the roundness of a bore, even when a quench-hardened part is formed in a direction of bore axis, by using a honing head, provided with grindstones having a part tilted for a cylinder bus in a grindstone holder so as to come into contact with at least one quench-hardened part despite a position in a circumferential direction, to perform honing work.

CONSTITUTION: A grindstone 18 in a honing head 16 has a part tilted for a cylinder bus in a grindstone holder 20, that is, a part helically arranged. Thus in whatever position in a circumferential direction the grindstone 18 is placed, at least its one part is placed in a condition coming into contact with a quench- hardened part 14. That is, a condition, that the grindstone 18 is brought into contact only with a part of low hardness between the quench-hardened parts 14, is prevented from being generated. Accordingly, a protruding amount of the grindstone 18, pressed to the outer in a radial direction by a spring, for instance, is determined by the quench-hardened part 14 of high hardness, and a fixed value of a cutting amount is obtained over the total periphery of a bore 12. As a result, roundness of the bore 12 is obtained in a very high degree.