The most important performance requirement of a traverse mechanism is that the thickness of the silk package formed by the traverse mechanism is uniform or has little variation in the centre. To realize this requirement and overcome the structural shortcomings of traditional traverse mechanisms, a new kind of traverse mechanism is proposed in this paper. The proposed mechanism is characterized by a non-circular gear drive formed by an eccentric gear and a conjugated two-lobed non-circular gear. Its kinematic model is deduced, together with a calculation model for the formed shape of the silk package cross-section. Both of these models contain the influence caused by the shift motion. Based on these two models, a computer-aided analysis program for the traverse mechanism, using MATLAB, is developed and the influences of the mechanical parameters on the formed shape of the silk package are analyzed. Furthermore, the mechanical parameters based on the new traverse mechanism give a better performance when compared with the traditional mechanism.