The flight dynamics model of air-breathing hypersonic vehicles (AHVs) is highly nonlinear and multivariable cou-pling, and includes inertial uncertainties and exteal disturbances that require strong, robust, and high-accuracy controllers. In this paper, we propose a linear-quadratic regulator (LQR) design method based on stochastic robustness analysis for the longitudinal dynamics of AHVs. First, input/output feedback linearization is used to design LQRs. Second, subject to various system parameter uncertainties, system robustness is characterized by the probability of stability and desired performance. Then, the mapping rela-tionship between system robustness and LQR parameters is established. Particularly, to maximize system robustness, a novel hybrid particle swarm optimization algorithm is proposed to search for the optimal LQR parameters. During the search iteration, a Cheoff bound algorithm is applied to determine the finite sample size of Monte Carlo evaluation with the given probability levels. Finally, simulation results show that the optimization algorithm can effectively find the optimal solution to the LQR parameters.