The conventional tooth surface of a face gear is difficult to manufacture, and the cutter is not uniform even though the parameters of its mating pinion slightly change. Based on the analysis of the features of the tooth surface, a new developable ruled surface approach is proposed that defines the tooth flank of the face gear, for which the most important feature is that it could be generated by a straight-edged cutter. This study presents mathematical models of the cutter and the new tooth surface and the corresponding deviation, correction and generation method for this surface, which are investigated through numerical examples. The manufacturing process is simulated by VERICUT software, and the results demonstrate that even when the principle deviation is added to the machined deviation, the absolute deviation is on the microscale. The meshing and contact simulation shows that the new surface could obtain good meshing performance when the number of face gear teeth is greater than three times the number of pinion teeth. This research provides a new method for manufacturing face gears.