In　this　paper,　we　propose　and　analyze　a　4-point　finite　volume　method　for　a　fracture　model　coupling　one-dimensional　equations　in　the　fracture　with　two-dimensional　equations　in　surrounding　domains.　The　pressure　is　approximated　in　the　piecewise　constant　spaces,　whereas　the　velocity　is　calculated　by　the　lowest　order　Raviart-Thomas　elements　and　piecewise　constants　in　matrix　and　fracture,　respectively.　Optimal　order　error　estimates　are　proved　on　nonuniform　triangular　meshes　for　both　the　pressure　and　velocity.　Beside,　we　extend　the　4-point　finite　volume　method　to　nonmatching　grids　between　the　fracture　and　matrix　without　loss　of　any　accuracy.　Numerical　experiments　on　matching　and　nonmatching　meshes　are　tested　for　models　with　higher,　lower　and　anisotropic　fracture　permeability,　and　results　confirm　our　theoretical　analysis.　(C)　2019　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.