Community　structure　is　a　very　important　characteristic　of　complex　networks,　detecting　communities　within　networks　has　very　important　significance　in　several　disciplines　like　computer　science,　physics,　biology,　etc.　To　some　extent,　Real-world　networks　exhibit　overlapping　community　structure.　To　solve　this　problem,　we　devise　a　novel　algorithm　to　identify　overlapping　communities　in　social　networks　with　Grey　Relational　Analysis.　This　paper　presents　the　edge　vector　which　is　a　measure　of　relationships　among　nodes,　and　uses　balanced　closeness　degree　to　describe　edge　similarity,　computes　edge　clusters　and　finally　obtains　overlapping　community　structure.　The　effectiveness　and　the　efficiency　of　the　new　algorithm　is　evaluated　by　experiments　on　both　real-world　and　the　computer-generated　datasets.