CO2-EOR　in　a　geological　formation　not　only　increases　oil　production　but　also　ensures　geological　sequestration　of　CO2.　The　capillary　pressure　is　an　essential　factor　during　the　process　of　immiscible　CO2-EOR　in　fractured　media.　Two　classical　capillary　pressure　models　are　adopted　to　investigate　the　effects　systematically　based　on　a　unified　pipe-network　method.　The　identical　capillary　pressures　in　fractures　and　the　rock　matrixes　have　little　effect　on　the　fluid　flow　and　saturation　distribution　of　CO2.　This　implies　that　the　capillary　pressure　can　be　neglected　in　this　condition.　The　effect　cannot　be　ignored　when　different　capillary　pressures　are　assigned　for　fractures　and　rock　matrixes.　The　saturation　of　CO2　reaches　its　highest　value　at　the　fracture　outlet　tip　if　the　capillary　pressure　in　a　fracture　is　smaller　than　that　in　the　rock　matrix.　The　phenomenon　of　saturation　concentration　of　CO2　at　the　fracture　tip　is　caused　by　the　capillary　pressure　difference.　For　non-connected　fractures,　the　saturation　concentration　causes　CO2　to　enter　the　adjacent　fractures　more　easily.　Thus,　the　capillary　pressure　difference　enlarges　the　effect　of　fractures　on　the　CO2　flow,　and　shorten　the　breakthrough　time　of　CO2.　Hence,　both　the　storage　amount　of　CO2　and　the　production　of　oil　in　geological　media　are　reduced.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.