A　unified　pipe-network-based　numerical　manifold　method　(NMM)　is　developed　to　simulate　immiscible　two-phase　flow　in　a　geological　medium.　Both　heterogeneous　and　non-heterogeneous　geological　media　can　be　discretized　as　numerical　pipe　networks,　which　have　high　efficiency　and　accuracy　in　simulating　fluid　and　mass　transfer　in　fractured　rock　masses.　A　manifold　element　method　is　developed　to　solve　the　governing　equations　of　immiscible　two-phase　flow　in　pipes.　The　developed　NMM　can　simulate　moving　and　deforming　of　two-phase　flow　interface.　A　grid-based　front-tracking　method　updates　the　marker　points　constructing　the　fluid　interface　explicitly　in　each　time　step.　The　effectiveness　of　the　NMM　is　verified　through　analytical　and　finite　element　analysis.　Parametric　studies　are　conducted　by　simulating　immiscible　two-phase　flows　with　various　fluid　properties　in　homogeneous　and　inhomogeneous　geological　conditions.　The　results　show　that　the　developed　method　can　efficiently　simulate　the　moving　interface　of　two-phase　flow　in　geological　media,　including　effects　such　as　＂viscous　fingering＂,　a　noteworthy　phenomenon　in　enhanced　oil　recovery.　When　the　mobility　of　the　driving　fluid　is　larger　than　that　of　the　driven　fluid,　the　inhomogeneity　of　the　medium　can　cause　the　fluid　interface　to　roughen,　which　increases　over　time　during　the　process　of　two-phase　flow.　For　the　inverse　situation,　although　the　fluid　interface　remains　rough,　the　roughness　variation　throughout　the　process　is　not　prominent.