This　paper　investigates　the　problem　of　delay-dependent　robust　H　∞　filtering　for　uncertain　linear　systems　with　time-varying　delay.　Given　a　stable　system　with　parameter　uncertainties　residing　in　a　polytope　with　s　vertices,　the　focus　is　on　designing　a　robust　H∞　filter　such　that　the　filtering　error　system　is　robustly　asymptotically　stable　with　a　prescribed　H∞　noise　attenuation　level.　The　main　technique　used　is　the　free-weighting　matrix　method　by　considering　the　additional　useful　terms.　As　a　result,　an　improved　linear　matrix　inequality-based　delay-dependent　stability　criterion　is　obtained,　which　is　less　conservative.　Finally,　two　examples　have　been　presented　to　illustrate　the　effectiveness　of　the　proposed　methodology.　©　2009　IEEE.