A robust optimal trajectory design method is proposed in this paper. Genetic Algorithm (GA) is employed to optimize the whole trajectory to improve the terminal attack performance. To enhance the robustness of the trajectory to disturbances, the min-max method is integrated into the GA optimization process. The proposed approach is carefully illustrated with the robust optimization design of the trajectory for a portable short-range top-attack (PSRTA) missile. The $H_{infty}$ robust gainscheduled technique is used to design the attitude tracking autopilot to facilitate the trajectory design. The damp feedback loop of the weakly-damped missile body is innovatively treated as the Linear Parameter Varying system (the controlled plant), which is good for practical use. The proposed robust optimal trajectory design method and the $H_{infty}$ robust gain-scheduled attitude tracking autopilot are demonstrated to be effective from the whole trajectory simulation results of the PSRTA missile, which also exhibit high applicability for practical engineering problems.