The　problem　of　a　non-fragile　H∞　filter　design　for　a　class　of　linear　systems　is　discussed.　The　designed　filter　is　assumed　to　be　with　multiplicative　filter　gain　variations.　Sufficient　and　necessary　conditions　for　the　existence　of　the　non-fragile　H∞　filter　are　given　by　using　linear　matrix　inequality　(LMI).　Numerical　examples　illustrate　the　feasibility　and　advantage　of　the　proposed　designs.