This　brief　deals　with　the　robust　filtering　problem　for　uncertain　linear　systems　with　delayed　states　and　outputs.　Both　time-invariant　and　time-varying　cases　are　considered.　For　the　time-invariant　case,　an　algebraic　Riccati　matrix　inequality　approach　is　proposed　to　design　a　robust　H∞　filter　such　that　the　filtering　process　remains　asymptotically　stable　for　all　admissible　uncertainties,　and　the　transfer　function　from　the　disturbance　inputs　to　error　state　outputs　satisfies　the　prespecified　H∞　norm　upper　bound　constraint.　We　establish　the　conditions　under　which　the　desired　robust　H∞　filters　exist,　and　derive　the　explicit　expression　of　these　filters.　For　the　time-varying　case,　we　develop　a　differential　Riccati　inequality　method　to　design　the　robust　filters.　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.