This gear cutting machine, which is equipped with a cutter (15), a cutter spindle motor (11) that causes, via a crank mechanism (13) and a cutter spindle (16), the cutter (15) perform a stroke operation, and a motor control unit (10) that controls the rotation angle of the cutter spindle motor (11), is provided with a relieving spindle motor (12) that causes the cutter (15) to move in the direction of a relieving spindle via a link mechanism (four-joint link mechanism (14)). The motor control unit (10) controls the rotation angle of the relieving spindle motor (12) on the basis of the rotation angle of the cutter spindle motor (11). Consequently, a gear cutting machine that accurately controls the relieving operation in accordance with a desired shape, such as crowning and tapering of a gear to be cut can be provided.