A new inverse design methodology for a variable cross-section shock waverider (VCSW) is proposed to extend the flexibility of waverider design based on the local-turning osculating cones method. The proposed waverider is designed to ride on the top of a variable cross-section shock wave, whose cross-sectional shape is an ellipse with different eccentricity ratios. The feasibility and effectiveness of this method are verified using inviscid computational fluid dynamics simulations. To investigate the influence of the eccentricity ratio on the shape and aerodynamic performance of waveriders, five VCSW cases with different eccentricity ratio distributions are derived and numerically analyzed in detail. The results demonstrate that the VCSW with an increasing eccentricity ratio along the streamwise direction has a larger volumetric efficiency but a smaller lift-to-drag ratio. There is a contradiction between the volumetric and aerodynamic performances, and the tradeoff should be considered in the design process. In addition, the growth rate of the eccentricity ratio along the streamwise direction is also an important factor to design VCSW, which can be used to improve the performance of hypersonic waverider vehicles.