To evaluate how the uncertain factors in the entry dynamics such as the navigation errors at the entry point affect the landing precision effectively, by introducing the Galerkin projection, a rapid landing error prediction method for Mars entry is proposed. In this method, the Polynomial Chaos are used to approximate the vehicle's states, and the problem is converted to a deterministic dynamical systems. Applying the method to a representative entry scenario of our country's future Mars entry mission, simulation results indicate that, compared with Monte Carlo method, the proposed method is able to predict the mean and covariance with little error and more computational efficiency.