In view of the shortcomings of involute gear drive,the advantages of synthetic face gear drive are summarized. The circular arc profile is applied to the face gear,and the gear drive with circular tooth profile is put forward. By means of theoretical analysis,numerical calculation and physical experiment,the design of the tooth surface of the circular tooth profile is carried out. Based on gear meshing theory and differential geometry theory,the tooth surface equation of the conjugate tooth profile of the basic tooth profile of the circular rack is modeled firstly,and then use the envelope forming theory to derive the equation of gear face machining arc face gear,and the cutter and circular arc tooth profile gear for each envelope forming work on tooth surface and the derivation of the face gear transition surface equation. Finally,the MATLAB software program is used to solve the set of tooth points and imported into the CATIA software. The EXCEL table with macro program runs the macro program and generates the contour curve in the CATIA software. And then the 3D physical tooth surface of the arc gear profile is obtained by surface fitting method. Compared with the simulation model of gear cutting envelope,the accuracy is verified.