In　this　paper,　we　propose　a　novel　Maxwell　dynamic　vibration　absorber　(DVA)　with　lever,　inerter,　and　grounded　stiffness.　Firstly,　the　governing　equation　of　the　coupled　system　is　established.　The　analytical　formula　of　the　amplitude　amplification　factor　of　the　primary　system　and　the　natural　frequencies　of　the　coupled　system　are　derived.　There　are　three　fixed　points　in　the　amplitude–frequency　response　curve　of　the　primary　system,　which　are　independent　of　damping.　Then,　based　on　H∞　optimization　criterion,　two　possible　optimal　parameter　designs　of　the　proposed　model　are　obtained.　Considering　the　practical　engineering　application　and　ensuring　the　stability　of　the　system,　the　optimal　grounded　stiffness　ratio　is　selected,　and　six　working　ranges　of　inerter–mass　ratio　are　calculated.　Furthermore,　the　performance　of　the　vibration　reduction　is　compared　for　six　cases.　It　is　found　that　when　the　values　of　the　mass　ratio,　lever　amplification　ratio,　and　inerter–mass　ratio　change　in　different　intervals,　and　the　optimal　grounded　stiffness　ratio　has　different　cases　of　negative,　zero,　and　positive　results.　Especially　when　the　stiffness　coefficient　of　the　viscoelastic　Maxwell　model　and　another　grounded　stiffness　are　positive　at　the　same　time,　the　vibration　absorption　effect　is　better　theoretically.　Finally,　comparing　with　the　traditional　DVAs,　the　performance　of　the　novel　DVA　is　better　under　harmonic　excitation　and　random　excitation.　The　results　could　provide　theoretical　guidance　for　the　design　of　inerter-based　Maxwell-type　DVA　with　a　lever　component.　©　2023　by　the　authors.