The　system　stiffness　of　a　negative　stiffness　membrane　structure　is　widely　investigated　in　metamaterial　research,　and　some　special　performances　have　been　achieved.　While　for　acoustics,　low-frequency　absorption　still　remains　a　big　issue,　so　in　this　work,　a　negative　stiffness　membrane　structure　with　its　theoretical　calculation　model　and　experimental　verification　of　sound　absorption　is　established.　Moreover,　the　nonlinear　stiffness　changes　of　the　thin　film　under　different　deformation　conditions　and　different　spacing　between　two　permanent　magnets　are　systematically　analyzed,　obtaining　the　theoretical　stiffness　analytical　equation　of　the　negative　stiffness　thin-film　structure　system.　Combined　with　finite　element　simulation　analysis,　the　stiffness　variation　rule　and　influencing　factors　of　the　negative　stiffness　membrane　system　are　discussed.　Specifically,　the　impact　of　the　mass　radius,　mass　thickness,　and　film　thickness　on　the　magnetic　force　and　system　stiffness　is　analyzed.　Based　on　the　acquired　testing　results,　the　proper　addition　of　the　magnetic　suction　structure　will　induce　a　shift　of　the　absorption　peak　to　a　lower　frequency　region.　This　work　provides　useful　insights　for　the　further　development　of　the　low-frequency　sound　absorption　theory　and　testing　prototype　with　a　negative　stiffness　membrane　structure.