An　elegant　quantum　version　of　least-square　support　vector　machine,　which　is　exponentially　faster　than　the　classical　counterpart,　was　given　by　Rebentrost　et　al.　using　the　matrix　inversion　algorithm　(HHL).　However,　the　application　of　the　HHL　algorithm　is　restricted　when　the　structure　of　the　input　matrix　is　not　well.　The　iteration　algorithms　such　as　the　Newton　method　are　widespread　in　training　the　classical　support　vector　machine.　This　paper　demonstrates　a　quantum　support　vector　machine　based　on　the　regularized　Newton　method　(RN-QSVM),　which　achieves　an　exponential　speed-up　over　classical　algorithm.　At　first,　the　regularized　quantum　Newton　algorithm　is　proposed　to　get　rid　of　the　constraint　of　input　matrix.　Then　we　train　the　RN-QSVM　by　using　the　regularized　quantum　Newton　algorithm　and　classify　a　query　sample　by　constructing　the　quantum　state.　Experiments　demonstrate　that　RNQSVM　respectively　provides　advantages　in　terms　of　accuracy,　robustness,　and　complexity　compared　to　QSLS-SVM,　LS-QSVM,　and　the　classical　method.