In　this　paper,　a　combined　numerical　method　consisting　of　the　mixed　finite　element　method　(MFE)　for　the　pressure　equation　and　the　discontinuous　Galerkin　(DG)　method　for　the　saturation　equation　is　proposed　to　solve　hybrid-dimensional　fracture　models　of　incompressible　two-phase　flow　in　porous　media.　The　hybrid-dimensional　fracture　models　treat　fractures　as　(　d　-　1)-　dimensional　interfaces　immersed　in　d-dimensional　matrix　domains　and　take　fluid　exchange　between　fractures　and　surrounding　matrix　into　account.　Fully　implicit　approximation　schemes　combining　the　MFE-DG　method　with　the　backward　Euler　time　discretization　for　the　models　with　both　a　single　fracture　and　an　intersecting　fractures　network　are　all　formulated　successfully.　The　stability　of　the　discrete　solution　is　analyzed,　and　optimal　error　estimates　in　H(div)-norm　for　the　velocity　and　in　L2-norm　for　the　pressure　are　derived,　as　well　as　in　the　discrete　H1-norm　for　the　saturation.　Numerical　experiments　with　a　single　fracture　and　a　T-junction　intersecting　fractures　network　are　conducted　to　verify　the　accuracy　of　our　theoretical　analysis.