This　paper　considers　the　H-infinity　consensus　problem　with　restricted　frequency-domain　specifications　(RFDs)　of　multi-agent　systems.　Using　a　linear　transformation,　the　consensus　problem　is　first　transformed　into　a　partial　stability　problem　of　a　reduced　dimensional　system.　Then　the　sufficient　and　necessary　conditions　are　given　for　H-infinity　consensus　with　RFDs　in　directed　networks,　subject　to　parameter　uncertainties　and　external　disturbances.　Moreover,　the　state　feedback　controller　gain　is　achieved　by　a　alternating　iteration　algorithm.　A　numerical　example　is　presented　to　illustrate　the　effectiveness　of　the　proposed　approach.