This　paper　deals　with　an　H∞　filter　design　problem　for　networked　uncertain　systems　with　random　time　delays.　As　the　sensors　and　filters　are　connected　via　a　limited　bandwidth　communication　channel,　a　system＇s　measurements　are　often　subject　to　randomly　varying　delays.　And　the　delays　are　assumed　to　be　the　linear　functions　of　the　stochastic　variables　that　satisfy　Bernoulli　random　binary　distribution.　The　sufficient　conditions　for　the　existence　of　full-　and　reduced-order　filters　are　presented,　thus,　guaranteeing　that　the　filter　error　systems　are　exponentially　mean-square　stable　and　have　a　prescribed　H∞　disturbance　attenuation　level　via　linear　matrix　inequalities　(LMIs).　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.