Trajectory planning under uncertain dynamics is critical for safety-critical systems like Unmanned Aerial Vehicles (UAVs), where uncertainties in aerodynamic force and control surface failure can lead to mission failure. This paper proposes a Multi-stage Robust Optimization (MRO) framework to address nonlinear trajectory planning with bounded but unknown parameters. By integrating first-order sensitivity analysis and sequential optimization, the proposed method ensures robustness against worst-case parameter deviations while maintaining high terminal accuracy. Unlike existing approaches, this paper explicitly quantifies uncertainty propagation through sensitivity bounds and divides long-term planning into sub-stages to reduce cumulative errors. Simulations on a UAV model with uncertainties in aerodynamic coefficients, wind fields and coefficients of control inputs demonstrate that MRO achieves high terminal state accuracy and strong robustness.