This　paper　presents　an　approach　in　which　grey　relational　analysis　with　entropy　weight　is　incorporated　into　particle　swarm　optimization　algorithm　(PSO)　in　order　to　allow　this　heuristic　to　handle　multi-objective　optimization　(MO).　In　our　algorithm,　grey　relational　analysis　is　used　to　guide　particles　flight　for　MOPSO,　and　entropy　weight　is　also　incorporated　into　grey　relational　analysis　in　order　to　enrich　the　exploratory　capabilities　and　realize　the　intelligence　evaluation.　The　proposed　approach　is　validated　by　using　several　test　functions　and　practical　optimal　example.　Results　indicate　that　the　improved　algorithm　is　effective,　has　the　characteristics　of　easy　realization,　fast　convergence　speed,　and　can　be　considered　a　viable　alternative　to　solve　MO　problems.