Hypersonic vehicles encounter a multitude of uncertain factors during flight, which significantly affect the control of their flight trajectories. To investigate the mechanism of how uncertain factors influence flight trajectories and compensate for the deviations in vehicle range caused by uncertain factors during guidance and control, this paper proposes an uncertainty analysis method for vehicle range based on an improved non-intrusive polynomial chaos expansion (NPCE) method, which establishes an analytical mapping relationship between the vehicle range and the uncertain factors, and compares the analysis results with the Monte Carlo method through numerical simulations. The comparison results demonstrate that the uncertainty analysis method proposed by this paper can quantitatively assess the impact of various uncertain factors on the vehicle range, and significantly reduce computational complexity while maintaining the same level of accuracy as the Monte Carlo method, thereby providing a rational basis for the robust design and optimization of hypersonic vehicle trajectories.