In　this　paper,　we　propose　a　framework　for　hybrid　privacy-preserving　clinical　decision　support　system　in　fog–cloud　computing,　called　HPCS.　In　HPCS,　a　fog　server　uses　a　lightweight　data　mining　method　to　securely　monitor　patients’　health　condition　in　real-time.　The　newly　detected　abnormal　symptoms　can　be　further　sent　to　the　cloud　server　for　high-accuracy　prediction　in　a　privacy-preserving　way.　Specifically,　for　the　fog　servers,　we　design　a　new　secure　outsourced　inner-product　protocol　for　achieving　secure　lightweight　single-layer　neural　network.　Also,　a　privacy-preserving　piecewise　polynomial　calculation　protocol　allows　cloud　server　to　securely　perform　any　activation　functions　in　multiple-layer　neural　network.　Moreover,　to　solve　the　computation　overflow　problem,　a　new　protocol　called　privacy-preserving　fraction　approximation　protocol　is　designed.　We　then　prove　that　the　HPCS　achieves　the　goal　of　patient　health　status　monitoring　without　privacy　leakage　to　unauthorized　parties　by　balancing　real-time　and　high-accurate　prediction　using　simulations.　©　2017　Elsevier　B.V.