In　this　paper,　we　present　and　analyze　a　finite　volume　method　based　on　the　Crouzeix-Raviart　element　for　the　coupled　fracture　model,　where　the　fluid　flow　is　governed　by　Darcy＇s　law　in　the　one-dimensional　fracture　and　two-dimensional　surrounding　matrix.　In　the　numerical　scheme,　the　pressure　in　the　matrix　and　fracture　is　respectively　approximated　by　the　Crouzeix-Raviart　elements　and　piecewise　constant　functions,　and　then　the　velocity　is　calculated　by　piecewise　constant　functions　element　by　element.　The　existence　and　uniqueness　of　the　numerical　solution　are　discussed,　and　optimal　order　error　estimates　for　both　the　pressure　p　and　the　velocity　u　are　proved　on　general　triangulations.　We　finally　carry　out　numerical　experiments,　and　results　confirm　our　theoretical　analysis.