Cloud　computing　is　very　useful　for　big　data　owner　who　doesn＇t　want　to　manage　IT　infrastructure　and　big　data　technique　details.　However,　it　is　hard　for　big　data　owner　to　trust　multi-layer　outsourced　big　data　system　in　cloud　environment　and　to　verify　which　outsourced　service　leads　to　the　problem.　Similarly,　the　cloud　service　provider　cannot　simply　trust　the　data　computation　applications.　At　last,　the　verification　data　itself　may　also　leak　the　sensitive　information　from　the　cloud　service　provider　and　data　owner.　We　propose　a　new　three-level　definition　of　the　verification,　threat　model,　corresponding　trusted　policies　based　on　different　roles　for　outsourced　big　data　system　in　cloud.　We　also　provide　two　policy　enforcement　methods　for　building　trusted　data　computation　environment　by　measuring　both　the　MapReduce　application　and　its　behaviors　based　on　trusted　computing　and　aspect-oriented　programming.　To　prevent　sensitive　information　leakage　from　verification　process,　we　provide　a　privacy-preserved　verification　method.　Finally,　we　implement　the　TPTVer,　a　Trusted　third　Party　based　Trusted　Verifier　as　a　proof　of　concept　system.　Our　evaluation　and　analysis　show　that　TPTVer　can　provide　trusted　verification　for　multi-layered　outsourced　big　data　system　in　the　cloud　with　low　overhead.