The actual tooth surface equation is established considering the worm wheel installation errors based on a five- axis linked CNC grinding machine. The tooth contact analysis（ TCA analysis） on the actual tooth surface of face gear and pinion tooth surface is investigated,and the solving method of contact point path of the face gear pair is obtained. The TCA analysis indicates that the tangential and axial linear position errors can cause deviation of the tooth surface along the tooth width and tooth height directions,also the contact point path has a larger deviation along the tooth length direction. The yaw angle errors can cause the tooth surface to incline along the tooth length direction,and there exists a bigger deviation as well as inclination along the tooth length direction. The pitch angle errors will cause the tooth surface to rotate along the tooth height direction,and the contact point path will rotate at the same time. The contact point path of face gear pair is much more sensitive to the four kinds of worm wheel installation errors. A theoretical reference for the error tracing in the face gear designing and manufacturing and the real tooth surface contact analysis is provided by the research.