Based on the theory of multi-body system and the principle of gear meshing,according to six-axis five linkage gear CNC machine structure and the actual conditions of grinding,the grinding tooth surface equation of face gear with error of six-axis five linkage CNC machine is established.Through the simulation,the influence of the grinding wheel spindle kinematic pair on different error sensitive direction is analyzed,the results show that the feed axis B5 relative to machine tool bed B1 moving has larger effect on the tooth profile machining of face gear.A prejudge theory for CNC grinding to improve the machining precision and modified tooth surface error is provided.