Market-based　measures,　like　the　carbon　cap-and-trade　(CCT)　scheme,　can　effectively　reduce　emissions　and　promote　green　technology　by　internalizing　the　external　costs　in　the　shipping　industry.　Under　the　CCT　scheme,　the　government　sets　the　quantity　commitment　of　carbon　emissions　for　a　unit　of　shipping　work,　and　the　excessive　quantity　must　be　traded　from　the　inner　shipping　market.　To　cope　with　carbon　regulation,　carriers　can　adjust　their　ship　deployment　plan　and　adopt　new　engine　technologies　to　support　low-carbon　fuels.　This　paper　proposes　a　bi-level　programming　model　to　investigate　the　effects　of　the　CCT　scheme　on　the　decisions　of　carriers　in　a　competitive　inland　container　shipping　network.　At　the　upper　level,　carriers　adjust　their　own　ship　deployment　plan　and　the　choice　of　technology　and　fuel　type.　At　the　lower　level,　the　shippers　between　different　origins　and　destinations　choose　the　shipping　lines　with　the　given　ship　deployment　plans　of　carriers.　Two　kinds　of　equilibrium　are　considered　in　the　proposed　problem:　the　competitive　equilibrium　of　carriers　on　freight　shipment　in　the　inland　shipping　network　and　the　trading　equilibrium　of　carbon　quotas.　The　former　equilibrium　can　be　captured　by　a　traffic　assignment　model　in　a　similar　transit　transportation　network,　and　the　latter　equilibrium　follows　the　idea　of　the　demand-supply　equilibrium　of　carbon　quotas　in　the　traditional　market.　The　two　equilibria　interact　since　the　freight　distribution　affects　the　shipping　revenue　of　each　ship　and　the　trading　equilibrium　is　related　to　the　total　cost　of　the　ship.　The　properties　of　the　optimal　choice　of　technology　and　fuel　type　are　theoretically　studied.　We　find　that　the　optimal　choice　of　fuel　technology　for　each　ship　assigned　to　any　shipping　line　at　any　given　CCT　must　be　Pareto　optimal　in　the　sense　of　cost-related　and　emission-relative　measures.　Based　on　the　result,　the　optimal　solution　of　the　proposed　model　can　be　calculated　by　a　sampling-based　method.　Numerical　examples　based　on　the　Yangtze　River　are　further　adopted　to　illustrate　the　proposed　model　and　conclusions.