We　investigate　the　effect　of　(interface)　surface　tensor　on　the　linear　Rayleigh-Taylor　(RT)　instability　in　stratified　incompressible　viscous　fluids.　The　existence　of　linear　RT　instability　solutions　with　largest　growth　rate　Lambda　is　proved　under　the　instability　condition　(i.e.,　the　surface　tension　coefficient　upsilon　is　less　than　a　threshold　upsilon(c))　by　the　modified　variational　method　of　PDEs.　Moreover,　we　find　a　new　upper　bound　for　Lambda.　In　particular,　we　directly　observe　from　the　upper　bound　that　Lambda　decreasingly　converges　to　zero　as　upsilon　goes　from　zero　to　the　threshold　upsilon(c).