This　paper　investigates　the　consensus　problem　of　large-scale　multi-agent　systems　(MASs)　with　a　directed　communication　topology,　especially　for　the　MAS　whose　topology　contains　small　strongly　connected　components.　A　sufficient　and　necessary　consensus　criterion　is　proposed　through　the　combination　of　two　methods.　Firstly,　a　communication　searching　algorithm　is　utilized　to　make　sure　that　each　agent　obtains　the　local　topology　information　of　strongly　connected　component　where　it　is　located.　Secondly,　a　state-linear-transformation　decomposes　the　consensus　problem　into　a　group　of　stability　problems　based　on　the　strongly　connected　components.　The　corresponding　consensus　criterion　reduces　the　computational　complexity.　Moreover,　according　to　the　consensus　criterion,　a　distributed　design　procedure　of　gain　matrices　is　proposed　based　on　the　homotopy　method.