In　this　paper,　we　present　a　discontinuous　finite　volume　method　for　a　hybrid-dimensional　coupled　fracture　model　on　triangular　meshes.　In　matrix　and　fracture,　the　pressure　is　approximated　by　the　discontinuous　and　continuous　piecewise　linear　elements,　and　in　order　to　retain　local　conservation　property,　the　velocity　is　sought　in　the　discontinuous　lowest-order　Raviart-Thomas　element　space　and　piecewise　linear　element　space.　The　proposed　numerical　scheme　is　only　associated　with　the　pressure,　so　we　avoid　solving　an　indefinite　saddle-point　problem.　In　addition,　the　discontinuous　method　eliminates　the　continuity　of　approximate　functions　across　the　interelement　boundary,　so　it　has　the　advantage　of　high　localizability　and　easy　handling　of　complicated　geometries.　Optimal　order　error　estimates　for　the　pressure　and　velocity　are　proved,　and　numerical　experiments　are　carried　out　to　confirm　our　theoretical　analysis.　(C)　2019　Published　by　Elsevier　Ltd.