The　paper　aims　at　discussing　the　set-valued　Choquet　integral,　which　is　the　integral　of　set-valued　random　variables　with　respect　to　capacities.　We　mainly　present　representation　theorems　of　the　set-valued　random　variable　by　using　a　sequence　of　Choquet　integrable　selections　and　then　we　investigate　some　properties　of　set-valued　Choquet　integrals,　especially　subadditive　property　and　inequality　of　the　metric　of　set-valued　Choquet　integrals.　We　also　prove　Fatou＇s　Lemmas,　Lebesgue　dominated　convergence　theorem　and　monotone　convergence　theorem　of　set-valued　Choquet　integrals　under　the　weaker　conditions　than　that　in　previous　works.　(C)　2012　Elsevier　B.V.　All　rights　reserved.