We investigate the pitching stability characteristics of sedan-type vehicles using large-eddy simulation (LES) technique. Pitching oscillation is a commonly encountered phenomenon when a vehicle is running on a road. Attributed to the change in a vehicle's position during pitching, the flow field around it is altered accordingly. This causes a change in aerodynamic forces and moments exerted on the vehicle. The resulting vehicle's response is complex and assumed to be unsteady, which is too complicated to be interpreted in a conventional wind tunnel or using a numerical method that relies on the steady state solution. Hence, we developed an LES method for solving unsteady aerodynamic forces and moments acting on a vehicle during pitching. The pitching motion of a vehicle during LES was produced by using the arbitrary Lagrangian-Eulerian technique. We compared two simplified vehicle models representing actual sedan-type vehicles with different pitching stability characteristics. The first phase of the simulations validated the numerical method adopted by comparing the flow structures, which was reproduced when a model was stationary, with wind tunnel visualizations. Then, a sinusoidal-forced-pitching oscillation was imposed on the models to probe their responses during pitching. The resulting aerodynamic pitching moment exerted on the models was phase averaged and decomposed into static, quasi-static, and dynamic components for evaluating their aerodynamic damping coefficients. This method successfully quantified the aerodynamic damping factors for vehicles subjected to pitching oscillation.