<p>In this paper, by combining the two-grid decoupled strategy and an existing domain decomposition method, two novel two-grid domain decomposition methods are constructed and analyzed for the coupled Navier–Stokes–Darcy model with Beavers–Joseph–Saffman interface condition. The proposed algorithms can decouple the Navier–Stokes–Darcy model into two independent Navier–Stokes and Darcy subsystems on both the coarse and fine grids, respectively, which can be solved in parallel with existing code and efficient solvers; hence, they could significantly enhance the computational efficiency. Numerical analysis indicates that both algorithms could reach the same convergence order as that of the standard Galerkin method with a proper configuration between the coarse grid size and the fine mesh size. Some numerical results are reported to show the main features of the two proposed algorithms.</p>