This　note　is　concerned　with　a　new　controller　design　problem　for　networked　systems　with　random　communication　delays.　Two　kinds　of　random　delays　are　simultaneously　considered:　i)　from　the　controller　to　the　plant,　and　ii)　from　the　sensor　to　the　controller,　via　a　limited　bandwidth　communication　channel.　The　random　delays　are　modeled　as　a　linear　function　of　the　stochastic　variable　satisfying　Bernoulli　random　binary　distribution.　The　observer-based　controller　is　designed　to　exponentially　stabilize　the　networked　system　in　the　sense　of　mean　square,　and　also　achieve　the　prescribed　H-infinity　disturbance　attenuation　level.　The　addressed　controller　design　problem　is　transformed　to　an　auxiliary　convex　optimization　problem,　which　can　be　solved　by　a　linear　matrix　inequality　(LMI)　approach.　An　illustrative　example　is　provided　to　show　the　applicability　of　the　proposed　method.