To facilitate a centering for aligning a grinding tool with a cylindrical hole when a part of the cylindrical hole is ground to a tapered hole.

A hone tool 14 enabling the grinding diameter of a grinding tool 34 therearound to be increased or decreased is attached to a spindle 11 which is rotatable and longitudinally movable in the axial direction through a joint 13 allowed to be eccentric while a drive shaft 16 and a driven shaft 17 are positioned parallel to each other. A workpiece 1 is affixed to the hone tool in the advancing direction, and the cylindrical hole 2 of the workpiece is disposed parallel to the hone tool. The hone tool is inserted into the cylindrical hole by moving forward, increased in diameter to bring the magnet into contact with the inner surface of the cylindrical hole, and centered. Next, the hone tool is moved backward while rotating in the cylindrical hole, gradually increased in grinding diameter while moving backward, and grinds the opening side portion of the cylindrical hole to a tapered hole 3. Also, the hone tool is increased in grinding diameter by an amount of removal in the next forward grinding step after the backward grinding step, moves forward while rotating, gradually reduced in grinding diameter while moving forward, and further grinds the tapered hole to a tapered shape. The backward grinding step and the forward grinding step of the hone tool are alternately performed repeatedly.