Abstract: Due to its outstanding aerodynamic performance, the waverider is considered as one of the effective ways to break through the current “lift-to-drag barrier”. It has become the research hotspot for hypersonic vehicle design. However, the traditional waverider is widely generated by a single shock wave, which cause the lack of compression efficiency. To solve the aforementioned problem, a multistage compression waverider design method for non-axisymmetric shock waves, has been proposed in this paper based the local-turning osculating cones method. With the help of multiple non-axisymmetric shock waves, the pre-compression effect of the waverider forebody is able to be fully exerted, and new design ideas for the design of hypersonic vehicles under complicated geometric conditions can be provided as well. The double compression waverider with two elliptic cone shock waves was specified as an example to introduce the new proposed method in detail. Three types of double elliptic cone compression waveriders with different eccentricities were designed under the same conditions. The numerical results demonstrate that under the inviscid conditions, the wall pressure obtained by the proposed design method is basically consistent with the CFD result. The maximum error of the corresponding aerodynamic parameters is about 0.3%, which proves the reliability of this new proposed design method. Compared with the double conical compression waverider, the waverider with eccentricity larger than one has better compression performance and lift-drag characteristics, but lower total pressure recovery coefficient and volumetric efficiency. In contrast, the double compression waverider with eccentricity less than one has larger total pressure recovery coefficient and volumetric efficiency, but lower compression performance and lift-to-drag characteristics. Additionally, the shock structure of the waverider under the viscous conditions remain essentially the same, and the corresponding two elliptic cone shock waves basically intersect at the bottom section. It reveals that this kind of waverider still owns wonderful “wave-ride” characteristics when the viscosity is taken into consideration.