In　this　paper,　we　study　numerical　methods　for　solving　a　multi-dimensional　fracture　model,　which　couples　n-dimensional　Darcy　flow　in　matrix　with　(n　-　1)-dimensional　Brinkman　flow　on　fracture.　A　two-grid　decoupled　algorithm　is　proposed,　in　which　the　mixed　model　is　decoupled　by　using　the　coarse　grid　approximation　to　the　interface　conditions,　and　then　efficient　singlemodel　solvers　are　applied　for　decoupled　Darcy　and　Brinkman　problems　on　the　fine　mesh.　Error　estimates　show　that　the　two-grid　decoupled　algorithm　retains　the　same　order　of　approximation　accuracy　as　the　coupled　one.　Numerical　experiments　in　two-dimensional　(2D)　and　three-dimensional　(3D)　geometries　are　conducted,　and　their　results　confirm　our　theoretical　analysis　to　illustrate　the　efficiency　and　effectiveness　of　the　proposed　method　for　solving　multi-domain　problems.