The　neural　network　has　been　widely　used　to　train　predictive　models　for　applications　such　as　image　processing,　disease　prediction,　and　face　recognition.　To　produce　more　accurate　models,　powerful　third　parties　(e.g.,　clouds)　are　usually　employed　to　collect　data　from　a　large　number　of　users,　which　however　may　raise　concerns　about　user　privacy.　In　this　paper,　we　propose　an　Efficient　and　Privacy-preserving　Neural　Network　scheme,　named　EPNN,　to　deal　with　the　privacy　issues　in　cloud-based　neural　networks.　EPNN　is　designed　based　on　a　two-cloud　model　and　techniques　of　data　perturbation　and　additively　homomorphic　cryptosystem.　This　scheme　enables　two　clouds　to　cooperatively　perform　neural　network　training　and　prediction　in　a　privacy-preserving　manner　and　significantly　reduces　the　computation　and　communication　overhead　among　participating　entities.　Through　a　detailed　analysis,　we　demonstrate　the　security　of　EPNN.　Extensive　experiments　based　on　real-world　datasets　show　EPNN　is　more　efficient　than　existing　schemes　in　terms　of　computational　costs　and　communication　overhead.