<p>In this paper, a two-grid domain decomposition method is proposed and investigated for the mixed dual-permeability-Stokes system by combing the existing robin-type domain decomposition method and the two-grid strategy. The proposed algorithm involves solving a mixed problem with existing robin-type domain decomposition method on a relatively coarse grid, then solving three independent subproblems on a fine grid via approximating the interface terms by the coarse grid approximation; they could be solved in parallel since these are decoupled. The incorporation of the domain decomposition method and two-grid decoupled method not only inherits the advantages of the both methods but also partly overcomes the defects of the both methods. Rigorously theoretical analysis is established and some comprehensively numerical experiments are reported to verify the features of the proposed algorithm.</p>