The paper proposed a new asymmetrical offset face-gear transmission, applied meshing theory to derive the tooth surface mathematical model, and used discrete numerical methods to obtain the tooth model. Subsequently, the limitation of pointing and undercutting on effective tooth width of asymmetric offset face-gear were studied, and the influence of the eccentricity on the effective tooth width was analyzed. Finally, the finite element method was used to analyze the tooth surface contact stress of four groups of asymmetric offset gear pairs with different working pressure angles. The conclusion shows that the tooth surface contact stress takes the minimum value when the working side pressure angle is 30°, and the contact stress significantly reduced compared to the face-gear pair that does not adopt an asymmetric structure. The research provides a reference to the design of asymmetric offset face-gear.