Abstract: The inflation process of a parachute involves complex fluid-structure interaction phenomena. The immersed boundary method, as a boundary non-conforming approach, is suitable for handling such nonlinear large deformation FSI problems. In this paper, the sharp-interface IB method proposed by Mittal et al. is coupled with the large eddy simulation to simulate flows over the parachute at medium to high Reynolds numbers. A dynamic Vreman sub-grid-scale model, suitable for complex geometries and non-uniform flows, is introduced for the SGS modeling. The accuracy of the developed LES/IB method is verified by the canonical flow over a circular cylinder at Re = 3900, and the grid independence and parallel computing performance of the fluid solver are analyzed for flows over a rigid parachute. Subsequently, an FSI simulation method for parachute inflation at medium to high Reynolds numbers is established by coupling the LES-IB fluid solver with a nonlinear finite element solid solver. The reliability of the FSI method for simulating parachute inflation is verified by analyzing and comparing the aerodynamic performance and structural response during the inflation process of typical round and cross parachutes.