In this study, aerodynamic design exploration for reusable launch vehicle (RLV) is conducted using genetic algorithm with Navier-Stokes solver to understand the aerodynamic characteristics for various body configurations and find design information such as tradeoff information among objectives. The multi-objective aerodynamic design optimization for minimizing zero-lift drag at supersonic condition, maximizing maximum lift-to-drag ratio (L/D) at subsonic condition, maximizing maximum L/D at supersonic condition, and maximizing volume of shape is conducted for bi-conical shape RLV based on computational fluid dynamics (CFD). The total number of evaluation in multi-objective optimization is 400, and it is necessary for evaluating one body configuration to conduct 8 CFD runs. In total, 3200 CFD runs are conducted. The analysis of Pareto-optimal solutions shows that there are various trade-off relations among objectives clearly, and the analysis of flow fields shows that the shape for the minimum drag configuration is almost the same as that of the shape for the maximum L/D configuration at supersonic condition. The shape for the maximum L/D at subsonic condition obtains additional lift at the kink compared with the minimum drag configuration. It leads to enhancement of L/D.