The　vibration　control　performance　of　a　combined　vibration　isolation　(CVI)　system　consists　of　a　quasi-zero　stiffness　(QZS)　system　and　a　linear　dynamic　vibration　absorber　(DVA)　is　investigated.　Firstly,　the　dynamic　equation　is　established　and　the　amplitude-frequency　response　of　the　CVI　system　is　deduced　by　the　harmonic　balance　method,　and　the　analytical　result　is　verified　by　numerical　simulation.　Secondly,　the　mechanism　of　CVI　system　is　revealed　from　the　perspectives　of　vibration　amplitude,　energy,　and　force　transmission:　The　vibration　isolation　performance　of　the　QZS　system　can　be　improved　by　reducing　the　vibration　amplitude.　Thirdly,　the　control　performance　of　the　CVI　system　is　analyzed　in　terms　of　the　effects　of　the　stiffness,　damping,　mass　ratio　of　DVA,　and　the　damping　of　the　primary　system,　as　well　as　the　robustness　of　the　system.　The　findings　lead　to　the　development　of　an　explicit　tuning　rule　for　the　DVA　attached　to　the　QZS　system.　Lastly,　a　comparison　of　control　performance　with　other　three　models　is　conducted.　The　results　demonstrate　that　the　CVI　system　can　effectively　suppress　the　vibration　amplitude　and　broaden　the　isolation　frequency　band.　The　mechanism　and　tuning　rule　for　the　CVI　system　presented　in　this　paper　provides　a　useful　reference　for　improving　the　control　performance　of　the　QZS　system.　©　2023　Elsevier　Ltd