A　novel　reconstruction　method　of　nanometer　micro-displacement　of　Fabry-Perot　(F-P)　interference　is　proposed　in　this　study.　Hilbert　transforms　are　performed　for　F-P　interference　fringes,　and　the　obtained　signal　performs　tangent　operation　with　the　original　signal.　Finally,　the　validity　of　the　proposed　algorithm　and　the　structure　are　verified　by　simulation　and　several　experimental　measurements　for　vibration.　Results　from　the　experiments　show　that　the　maximum　relative　error　is　4.9%.