The　minimum　spanning　tree　(MST)　of　a　graph　is　an　important　concept　in　network　design,　the　basic　MST　problem　can　be　solved　efficiently,　but　the　multi-criteria　MST　(mc-MST)　is　NP-hard　problem.　In　this　paper,　a　discrete　particle　swarm　optimization　(PSO)　approach　is　developed　to　deal　with　this　problem.　The　principles　of　mutation　and　crossover　operator　in　the　genetic　algorithm　(GA)　are　incorporated　into　the　proposed　PSO　algorithm　to　achieve　a　better　diversity　and　break　away　from　local　optima.　In　the　end,　an　enumeration　method　of　Chen＇s　is　used　to　evaluate　the　algorithm＇s　performance　and　the　results　show　that　this　algorithm　is　efficient　and　feasible.