This　paper　proposes　a　novel　damping　model　with　negative　stiffness　known　as　the　half-cycle　negative-stiffness　damping　model.　Analysis　of　a　single　degree　of　freedom　(SDOF)　system　demonstrated　that　the　half-cycle　negative-stiffness　damping　model　has　negative　stiffness　and　energy　dissipation.　The　equivalent　negative　stiffness　of　the　model　was　derived　from　the　frequency　response　analysis　of　the　system.　An　alternating　transmission　system　and　a　one-way　friction　system　were　developed　to　assemble　a　half-cycle　negative-stiffness　damping　device　(HCNSDD),　which　can　generate　a　half-cycle　negative-stiffness　damping　model.　A　mechanical　model　was　developed　to　represent　the　force-displacement　relationship　of　the　proposed　HCNSDD.　A　HCNSDD　specimen　was　manufactured　and　examined　using　experimental　tests.　The　HCNSDD　exhibits　half-cycle　negative-stiffness　damping　and　stable　mechanical　properties,　demonstrating　the　feasibility　and　effectiveness　of　the　proposed　HCNSDD.　Finally,　a　finite　element　simulation　approach　for　HCNSDD　was　presented,　and　the　performance　of　seismic　vibration　control　of　HCNSDD　was　evaluated　using　a　multidegree-of-freedom　system.