Based on the meshing principle of face gear drive, a surface equation has been established of the face gear with the installation error, thus obtaining the calculation method of the main curvature and contact stress of the tooth surface of face gear. On this basis, a respective analysis has been made of the influence of axial deviation error, axial angle error and axial staggered error on the contact trajectory and contact stress of the face gear drive. The results show that the contact stress decreases gradually from the addendum to the root under various error conditions. According to the error analysis, the shaft angle error and axial across error are the most important influential factors on the contact trajectory and contact stress of the face gear, when the angle error is negative or axis error is positive in its value, the contact stress simulation values are significantly higher than those normal contact stress without errors. Therefore, it is highly recommended that the upper and lower deviation of these two errors be strictly controlled when installing the face gear pair.