Abstract: The inflation process of a parachute involves complex fluid-structure interaction (FSI) phenomena. The immersed boundary (IB) method, as a boundary non-conforming approach, is suitable for addressing such nonlinear large-deformation FSI problems. By integrating the sharp-interface IB method proposed by Mittal et al. with large eddy simulation (LES), the flow around a parachute at medium to high Reynolds numbers (Re) was simulated. On this basis, a nonlinear finite element method was incorporated to develop an FSI approach based on the dynamic Vreman subgrid-scale (Vreman SGS) model, which was suitable for complex geometries and non-uniform turbulence, to simulate the parachute inflation process. Finally, the accuracy of the developed LES/IB method was validated by a classic cylinder flow case (Re = 3900). The results demonstrate that the LES/IB method achieves good agreement with direct numerical simulation (DNS), LES, and experimental data in terms of the mean drag coefficient (\bar C_D ), mean base pressure coefficient at the rear stagnation point (- \bar C_p,\rm b ), and Strouhal number (St), with errors all below 8%. Furthermore, the developed Vreman SGS model was employed to analyze the aerodynamic performance and structural response during the inflation of typical round and cruciform parachutes, and the results were compared with Smagorinsky SGS model. During the breathing phase of parachute inflation, the results of the drag coefficient and projected area calculated by both methods show good agreement, with relative errors within 5%, thereby validating the reliability of the proposed FSI method.