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In this paper, we propose a two-grid finite element method for solving the mixed Navier–Stokes/Darcy model with the Beavers–Joseph–Saffman interface condition. After solving a coupled nonlinear problem on a coarse grid, we sequentially solve decoupled and linearized subproblems on a fine grid and then correct the solution on the same grid. Compared with the existing work on the two-grid methods for the coupled model, our two-grid method allows a much higher order scaling between the coarse grid size H and the fine grid size h. Specifically, if a k-th order discretization is applied, by using h= H 2 k+ 1 k for k= 1, 2 and h= H k+ 1 k− 1 for k≥ 3, the final step two-grid solution errors in the energy norm are still optimal. Numerical experiments are also given to confirm the theoretical analysis.