Machine　learning,　particularly　the　neural　network　(NN),　is　extensively　exploited　in　dizzying　applications.　In　order　to　reduce　the　burden　of　computing　for　resource-constrained　clients,　a　large　number　of　historical　private　datasets　are　required　to　be　outsourced　to　the　semi-trusted　or　malicious　cloud　for　model　training　and　evaluation.　To　achieve　privacy　preservation,　most　of　the　existing　work　either　exploited　the　technique　of　public　key　fully　homomorphic　encryption　(FHE)　resulting　in　considerable　computational　cost　and　ciphertext　expansion,　or　secure　multiparty　computation　(SMC)　requiring　multiple　rounds　of　interactions　between　user　and　cloud.　To　address　these　issues,　in　this　article,　a　lightweight　privacy-preserving　model　training　and　evaluation　scheme　LPTE　for　discretized　NNs　(DiNNs)　is　proposed.　First,　we　put　forward　an　efficient　single　key　fully　homomorphic　data　encapsulation　mechanism　(SFH-DEM)　without　exploiting　public　key　FHE.　Based　on　SFH-DEM,　a　series　of　atomic　calculations　over　the　encrypted　domain,　including　multivariate　polynomial,　nonlinear　activation　function,　gradient　function,　and　maximum　operations　are　devised　as　building　blocks.　Furthermore,　a　lightweight　privacy-preserving　model　training　and　evaluation　scheme　LPTE　for　DiNNs　is　proposed,　which　can　also　be　extended　to　convolutional　NN.　Finally,　we　give　the　formal　security　proofs　for　dataset　privacy,　model　training　privacy,　and　model　evaluation　privacy　under　the　semi-honest　environment　and　implement　the　experiment　on　real　dataset　MNIST　for　recognizing　handwritten　numbers　in　DiNN　to　demonstrate　the　high　efficiency　and　accuracy　of　our　proposed　LPTE.