A gear machining apparatus and a gear machining method are provided. The gear machining apparatus performs cutting work for a workpiece and generates a gear by performing a feed operation of a gear cutter relative to the workpiece along a direction of an axis of the workpiece while synchronously rotating the gear cutter and the workpiece in a state in which an axis of the gear cutter is inclined with respect to a line parallel to the axis of the workpiece. The gear machining apparatus sets a correction angle to a first angle when cutting work for a second tooth flank is started after cutting work for a first tooth flank is finished, and moves the gear cutter from a first finish position to a second start position while rotating the workpiece and the gear cutter.