The waverider has an extensive application prospect in the design of hypersonic vehicles due to its excellent aerodynamic efficiency. However, it is known that the original cone-derived waverider is longitudinally unstable. To solve the problem, a design method for hypersonic quasi-waverider configuration is first proposed and then a genetic algorithm optimization framework is constructed to obtain optimum quasi-waveriders with different constraints. During the optimization, the aerodynamic performance is evaluated by an efficient aerodynamic model that considers the impacts of strong viscous interaction effects. Results from numerical simulations show that, for the optimum quasi-waveriders without constraints, good shock wave attachment along the leading edge is achieved, and the maximum lift-to-drag ratio (L/DL/D) is even higher than that of the original waverider. Optimized quasi-waveriders are also generated based on the constraints of volumetric efficiency and stability. The L/DL/D first increases and then decreases with the increase in volumetric efficiency. In addition, an interesting phenomenon is found that the L/DL/D is reduced almost linearly with the increase in the degree of stability at each design condition. Furthermore, a linear relationship is also constructed between the variation of L/DL/D with respect to degree of stability and the viscous interaction parameter V¯′V¯′.