The invention discloses a face gear numerical control machining device and a face gear numerical control machining method. The face gear numerical control machining device comprises a numerical control gear shaper, a numerical control working turntable, a transition transmission mechanism and a face gear workpiece; the numerical control gear shaper comprises a tool base, a tool body, a gear shaper cutter, a numerical control gear shaper revolution working turntable, a numerical control system and a motor; the tool body is connected with the tool base; the gear shaper cutter is connected with the tool body; a numerical control gear shaper revolution workbench is connected with the base; the numerical control working turntable is fixed on the gear shaper revolution workbench; the motor is connected with the numerical control working turntable through the transition transmission mechanism; the face gear workpiece is fixed on the numerical control working turntable; and the numerical control system is respectively connected with the tool base and the motor. When the face gear numerical control machining device works, the tool body moves on the tool base to realize feed movement of face gear shaping machining; the gear shaper cutter and the face gear workpiece rotate around axes of the gear shaper cutter and the face gear workpiece to realize the generating movement of face gear machining; the gear shaper cutter swings to realize the cutter relieving movement of the face gear shaping machining; and the gear shaper cutter reciprocates up and down to realize the main cutting movement of the face gear shaping machining. The face gear numerical control machining device can realize high-efficiency and high-precision machining of the face gear.