Face-gear drives become the main direction of research for aeronautical drives because of their special advantages. The applied coordinate systems of face-gear were set up and the equation of face-gear tooth surface was established, then the face-gear tooth surface constrain conditions for dedendum undercutting and addendum pointing were analyzed based on the face-gear transmission theory, at the same time, the disciplines were discussed on the relationships between pressure angle and the face-gear outer & inner radius in keeping with the practically calculated examples. The calculating results are useful for designing the face-gear drive. In the end, the face-gear hobbing theory was analyzed, according to the gear geometry and applied theory, the hobbing surface equation was founded. The discrete values of three-dimensional coordinates for the hobbing surface were calculated by using the method of numerical calculation. The three-dimensional basal worm model of face-gear hob was designed by recurring to the three-dimensional software.