Based on the tooth cutting principle and manufacturing method of Oerlikon's hypoid gear, the structure and assembly location of three-faced blade is analyzed and the method to establish the mathematical model of three-face cutter head and plate (SPIRON) by the normal benchmark of the NS plane of tool is proposed. According to the manufacturing coordinate systems through HFT methods, the mathematical models of pinion with generating method and gear with shaping method is established on the basis of the NS benchmark. Furthermore, the technological process of Oerlikon's hypoid gear modeling based on the three-face cutter is proposed. The two compare methods were made between the mathematical tooth flank by tooth surface mathematical model and 45 point tooth surface by the KIMOS of both pinion and gear and the contact pattern with actual and theory. Results reveal that the geometry and tooth line of theoretical tooth surface of gear and pinion corresponds well with the actual tooth surface, the maximum the concave error of pinion was 0.007 5 mm,the maximum convex error of gear about 0.002 3 mm. The contact pattern is consistent between the contact patterns of tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) by KIMOS and calculated by the initial element method, it verified the precision of the mathematical model.