In　this　paper,　we　show　that　every　convex　semi-infinite　vector　optimization　(CSVO　for　brevity)　problem　can　be　arbitrarily　approximated　by　stable　CSVO　problems,　i.e.,　the　set　of　all　stable　CSVO　problems　(the　weak　solution　map　is　continuous　or　the　solution　map　is　upper　semicontinuous)　is　dense　in　the　set　of　all　CSVO　problems　with　the　given　topology.　(C)　2011　Elsevier　B.V.　All　rights　reserved.