Most　of　the　extant　studies　in　social　recommender　system　are　based　on　explicit　social　relationships,　while　the　potential　of　implicit　relationships　in　the　heterogeneous　social　networks　remains　largely　unexplored.　This　study　proposes　a　new　approach　to　designing　a　recommender　system　by　employing　grey　relational　analysis　on　the　heterogeneous　social　networks.　It　starts　with　the　establishment　of　heterogeneous　social　networks　through　the　user-item　bipartite　graph,　user　social　network　graph　and　user-attribute　bipartite　graph;　and　then　uses　grey　relational　analysis　to　identify　implicit　social　relationships,　which　are　then　incorporated　into　the　matrix　factorization　model.　Five　experiments　were　conducted　to　test　the　performance　of　our　approach　against　four　state-ofthe-art　baseline　methods.　The　results　show　that　compared　with　the　baseline　methods,　our　approach　can　effectively　alleviate　the　sparsity　problem,　because　the　heterogeneous　social　network　provides　richer　information.　In　addition,　the　grey　relational　analysis　method　has　the　advantage　of　low　requirements　for　data　size　and　efficiently　relieves　the　cold　start　problem.　Furthermore,　our　approach　saves　processing　time,　thus　increases　recommendation　efficiency.　Overall,　the　proposed　approach　can　effectively　improve　the　accuracy　of　rating　prediction　in　social　recommendations　and　provide　accurate　and　efficient　recommendation　service　for　users.