Training　data　distributed　across　multiple　different　institutions　is　ubiquitous　in　disease　prediction　applications.　Data　collection　may　involve　multiple　data　sources　who　are　willing　to　contribute　their　datasets　to　train　a　more　precise　classifier　with　a　larger　training　set.　Nevertheless,　integrating　multiple-source　datasets　will　leak　sensitive　information　to　untrusted　data　sources.　Hence,　it　is　imperative　to　protect　multiple-source　data　privacy　during　the　predictor　construction　process.　Besides,　since　disease　diagnosis　is　strongly　associated　with　health　and　life,　it　is　vital　to　guarantee　prediction　accuracy.　In　this　paper,　we　propose　a　privacy-preserving　and　high-accurate　outsourced　disease　predictor　on　random　forest,　called　PHPR.　PHPR　system　can　perform　secure　training　with　medical　information　which　belongs　to　different　data　owners,　and　make　accurate　prediction.　Besides,　the　original　data　and　computed　results　in　the　rational　field　can　be　securely　processed　and　stored　in　cloud　without　privacy　leakage.　Specifically,　we　first　design　privacy-preserving　computation　protocols　over　rational　numbers　to　guarantee　computation　accuracy　and　handle　outsourced　operations　on-the-fly.　Then,　we　demonstrate　that　PHPR　system　achieves　secure　disease　predictor.　Finally,　the　experimental　results　using　real-world　datasets　demonstrate　that　PHPR　system　not　only　provides　secure　disease　predictor　over　ciphertexts,　but　also　maintains　the　prediction　accuracy　as　the　original　classifier.　©　2019