This　study　concerns　the　Darcy　flow　problem　in　a　two-dimensional　fractured　porous　domain,　in　which　the　fracture　is　regarded　as　a　one-dimensional　interface,　interacting　with　the　surrounding　media.　In　this　paper,　a　finite　volume　element　method　(FVEM)　is　first　proposed　for　the　multi-dimensional　fracture　model,　and　error　estimates　for　the　pressure　with　optimal　convergence　are　discussed.　On　this　basis,　a　two-grid　FVEM　is　developed　for　decoupling　the　multi-domain　fracture　model　by　a　coarse　grid　approximation　to　the　interface　coupling　conditions,　and　theoretical　analysis　demonstrates　that　approximation　accuracy　does　not　deteriorate　under　the　two-grid　decoupling　technique.　Finally,　numerical　experiments　for　FVEM　and　two-grid　FVEM　are　presented　to　confirm　the　accuracy　of　theoretical　analysis.　(c)　2021　Elsevier　B.V.　All　rights　reserved.