A machining section (12) of a gear machining apparatus includes a workpiece support in the form of a shaft (J1) that pivotally supports the workpiece gear (14) and a cutter support in the form of a shaft (J2) that supports the chamfering cutter (18) so that the chamfering cutter (18) meshes with the workpiece gear (14) attached to the shaft (J1). The shaft (J1) is angled so that the chamfering cutter (18) meshes with the workpiece gear (14) at an axis-crossing angle ( ) not being zero degree and machining teeth (32a, 32b) of the chamfering cutter (18) do not interfere with a tooth face (28) of the workpiece gear (14). A gear machining method is also provided.
