With　the　proliferation　of　machine　learning,　the　cloud　server　has　been　employed　to　collect　massive　data　and　train　machine　learning　models.　Several　privacy-preserving　machine　learning　schemes　have　been　suggested　recently　to　guarantee　data　and　model　privacy　in　the　cloud.　However,　these　schemes　either　mandate　the　involvement　of　the　data　owner　in　model　training　or　utilize　high-cost　cryptographic　techniques,　resulting　in　excessive　computational　and　communication　overheads.　Furthermore,　none　of　the　existing　work　considers　the　malicious　behavior　of　the　cloud　server　during　model　training.　In　this　paper,　we　propose　the　first　privacy-preserving　and　verifiable　support　vector　machine　training　scheme　by　employing　a　two-cloud　platform.　Specifically,　based　on　the　homomorphic　verification　tag,　we　design　a　verification　mechanism　to　enable　verifiable　machine　learning　training.　Meanwhile,　to　improve　the　efficiency　of　model　training,　we　combine　homomorphic　encryption　and　data　perturbation　to　design　an　efficient　multiplication　operation　for　the　encryption　domain.　A　rigorous　theoretical　analysis　demonstrates　the　security　and　reliability　of　our　scheme.　The　experimental　results　indicate　that　our　scheme　can　reduce　computational　and　communication　overheads　by　at　least　43.94%　and　99.58%,　respectively,　compared　to　state-of-the-art　SVM　training　methods.