This　paper　is　devoted　to　the　continuity　of　solution　maps　for　perturbation　semi-infinite　vector　optimization　problems　without　compact　constraint　sets.　The　sufficient　conditions　for　lower　semicontinuity　and　upper　semicontinuity　of　solution　maps　under　functional　perturbations　of　both　objective　functions　and　constraint　sets　are　established.　Some　examples　are　given　to　analyze　the　assumptions　in　the　main　result.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.