A　novel　dynamic　vibration　absorber(DVA)　model　with　negative　stiffness　and　inerter-mass　is　presented　and　analytically　studied　in　this　paper.　The　research　shows　there　are　still　two　fixed　points　independent　of　the　absorber　damping　in　the　amplitude　frequency　curve　of　the　primary　system　when　the　system　contains　negative　stiffness　and　inerter-mass.　The　optimum　frequency　ratio　is　obtained　based　on　the　fixed-point　theory.　In　order　to　ensure　the　stability　of　the　system,　it　is　found　that　inappropriate　inerter　coefficient　will　cause　the　system　instable　when　screening　optimal　negative　stiffness　ratio.　Accordingly,　the　best　working　range　of　inerter　is　determined　and　optimal　negative　stiffness　ratio　and　approximate　optimal　damping　ratio　are　also　obtained.　At　last　the　control　performance　of　the　presented　DVA　is　compared　with　three　existing　typical　DVAs.　The　comparison　results　in　harmonic　and　random　excitation　show　that　the　presented　DVA　could　not　only　reduce　the　peak　value　of　the　amplitude-frequency　curve　of　the　primary　system　significantly,　but　also　broaden　the　efficient　frequency　range　of　vibration　mitigation.