A multi-objective genetic algorithm (MOGA) has been applied to the multidisciplinary design optimization (MDO) of a launch vehicle (LV) with a hybrid rocket engine (HRE) to investigate the ability of an HRE to serve as a sounding rocket from various perspectives. In this study, the flight evaluation was enhanced to 3-degree-of-freedom (3DoF) in order to consider the equations of motion for horizontal and vertical motion and rotation of the LV. In the consideration of the rotation of the LV, the time variation of the center of gravity due to the fuel burn was estimated. The non-dominated sorting genetic algorithm-II (NSGA-II) was used to solve multi-objective problems (MoPs). Four design problems were examined in order to understand the practical physics of hybrid rocket. As a result, tradeoff information was observed for all design problems. The results for the present four design problems indicate that economical performance of LV is limited with the HRE in terms of the maximum altitude and maximum downrange distances achievable. The hypervolume, which was used as the metric to evaluate the difficulty of the design problems, reveals that the convergence of the solutions for not only altitude maximization in the case of a vertical launch but also the maximization of downrange at higher target altitudes was affected by the severe limitation. To observe the dependence of the design problems on the constraint, the design problems were visualized using a colored parallel coordinates plot (PCP), and the LV geometries determined from the nondominated solutions were successfully examined.