The tooth surface modeling,cutting simulation and finite element analysis of hypoid gears cut by the completed method is studied,which the wheel gear is cut by the format method while the gear is generated by the duplex helical method. The pinion tooth surface equation can be derived based on the coordinates transformation and spatial meshing theory. According to machine-tool settings of Gleason’s summary,the high-precision solid model of gear pairs can be established by the cutting simulation of the generated motion between cutter and blank in CATIA software package. By using the finite element software Abaqus to conduct the contact analysis of gears drive,and the tooth root bending stress and the tooth surface contact stress can be calculated and extracted in the entire meshing process,the research results can provide a reference for the strength design of hypoid gear.