This paper presents a novel computational approach for quantifying the propagation of the uncertainties in the state trajectories of low-lift Mars entry vehicle. The unique contribution of this work is twofold: one is considering the change of stochastic characteristics due to the high nonlinearity of Mars entry dynamics to improve propagation accuracy, and the other is suppressing the increase of equation dimension in long-term integration to enhance computational efficiency. Generalized polynomial chaos is modified accordingly through conducting spectral decomposition and random space decomposition adaptively. In this framework, stochastic dynamics is modeled and transformed into equivalent deterministic dynamics in higher-dimensional space and is updated adaptively when the statistic characteristic of system state changes greatly. The random space is decomposed adaptively when the relative error in variance becomes larger than the predefined threshold. In each random sub-domain, the updated generalized polynomial chaos is employed. We demonstrate that the proposed method is able to quantify propagation of uncertainty effectively in Mars atmospheric entry dynamics, with a better accuracy level than generalized polynomial chaos and much more computational efficiency than Monte-Carlo simulations. Meanwhile, the influences and the evolution profiles of the initial and parametric uncertainties during Mars entry are revealed through parametric studies.