We　propose　a　novel　time-stepping　scheme　for　solving　the　Allen-Cahn　equation.　We　first　rewrite　the　free　energy　into　an　equivalent　form　and　then　obtain　a　new　Allen-Cahn　equation　by　energy　variational　formula　of　L2-gradient　flow.　Using　leapfrog　formula,　a　new　linear　scheme　is　obtained,　and　we　prove　that　the　numerical　scheme　is　unconditionally　energy　stable　and　uniquely　solvable,　and　the　discrete　energy　is　in　agreement　with　the　original　free　energy.　In　addition,　we　also　discuss　the　uniform　boundedness　and　error　estimate　of　numerical　solution,　the　results　show　that　the　numerical　solution　is　uniformly　bounded　in　H2-norm,　and　error　estimate　shows　that　the　time-stepping　scheme　can　achieve　second-order　accuracy　in　time　direction.　At　last,　several　numerical　tests　are　illustrated　to　verify　the　theoretical　results.　The　numerical　strategy　developed　in　this　paper　can　be　easily　applied　to　other　gradient　flow　models.　©　2022　Shimin　Lin　et　al.