An　improved　algorithm　focusing　on　Berman′s　approximation　when　k　is　equal　to　3　is　proposed.　After　solving　the　shortest　distance　of　each　pair　of　points　for　the　corresponding　set　by　using　Fibonacci　heap,　a　Voronoi　region　is　created　to　find　the　cost　of　triple　subtree,　then　the　network　topology　structure　of　the　Steiner　tree　is　analyzed　to　cut　off　useless　triples.　The　proposed　method　can　simplify　the　topology　structure　and　reduce　the　time　complexity.　The　experiment　results　show　that　many　useless　triples　can　be　filtered　before　beginning　of　the　evaluation　and　construction　phase,　and　the　filter　factor　is　higher　than　0.9　for　each　example,　some　even　up　to　0.999.　With　the　decrease　of　the　running　time,　it　shows　that　the　improved　algorithm　is　much　more　effective　for　applications　in　routing　multicast.