The worm gear set, which is composed of a worm and worm gear, is one of the cross axes transmission mechanisms. Based on the cutting method and the asymmetric straight-sided cutter, the mathematical model of the asymmetric ZN-type worm surfaces is developed. The mathematical model of the worm gear surfaces can be obtained by applying the cutting mechanism of the worm gear hobbing process and the equation of meshing between the hob cutter and the produced worm gear surfaces. Based on the developed mathematical model of the worm gear set surfaces, the tooth contact analysis of the worm gear set is performed and the finite element stress analysis is also investigated. By comparing the analysis results of an asymmetric ZN-type worm gear set with a symmetric ZN-type worm gear set, it is most helpful to the design and manufacture of the worm gear sets. It is found that the strength of the asymmetric ZN-type worm gear set is higher than that of the symmetric ones. Therefore, the asymmetric ZN-type worm set is suitable for one direction rotation transmissions.