With　the　enhanced　capabilities　of　the　SCADA　system,　the　power　system　can　monitor　its　operating　states　in　real-time.　On　the　other　hand,　it　also　makes　the　power　system　more　vulnerable　to　various　kinds　of　attacks.　One　attack　that　has　serious　consequences　is　the　False　Data　Injection　(FDI)　attack　against　the　state　estimation　process.　Although　some　techniques　have　been　proposed　to　select　meters　to　protect,　none　of　them　considers　the　cost　of　protecting　meters,　and　thus　will　not　perform　well　when　only　a　limited　number　of　meters　can　be　protected　due　to　budget　limitation.　In　this　paper,　we　consider　a　new　problem:　Given　a　limited　budget,　how　to　select　the　most　critical　meters　to　protect　so　that　the　probability　of　attackers　launching　successful　stealthy　FDI　attack　is　minimized＇)　We　first　formalize　this　problem　which　is　NP-complete,　and　then　propose　heuristic　based　solutions.　The　idea　is　to　rank　and　select　meters　based　on　a　metric　called　vulnerability　index,　which　considers　two　factors:　how　likely　the　meter　will　be　targeted　by　the　attacker　to　launch　FDI　attacks　and　how　much　damage　will　be　caused　by　compromising　the　meter　in　case　of　a　successful　stealthy　FDI　attack.　Evaluation　results　show　that　our　algorithm　can　significantly　reduce　the　probability　of　successful　attacks,　as　well　as　the　potential　damage　caused　by　FDI　attacks.