The　sensors　and　filter　are　connected　via　a　limited　bandwidth　communication　channel.　The　system　measurements　are　often　subject　to　randomly　varying　communication　delays.　A　H-infinity　filtering　problem　is　proposed　for　linear　discrete-time　networked　systems　with　random　communication　delays.　The　problem　addressed　here　is　the　design　of　a　linear　H-infinity　filter　such　that　the　error　systems　are　exponentially　mean-square　stable　and　guarantee　a　prescribed　H-infinity　performance　in　term　of　linear　matrix　inequality　(LMI).　The　filter　is　then　obtained　by　solving　a　LMI　using　convex　optimization　techniques.　A　numerical　example　is　also　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.