Basing　on　the　posteriori　error　estimation　and　Superconvergent　Patch　Recovery　(SPR)　technology,　Elena　Zhelezina　proposed　a　fast　adaptive　mesh　refinement　strategy　which　can　generate　the　refined　mesh　for　the　required　accuracy　of　the　solution　with　only　one　step　of　refining　the　initial　mesh.　However,　this　remeshing　strategy　still　generates　too　many　elements　which　will　spend　too　much　memory　and　CPU　time　to　solve　the　FEM　sparse　matrices.　In　this　paper,　a　new　formula　to　estimate　the　global　error　is　introduced,　and　then,　a　new　strategy　to　calculate　every　element＇s　refinement　degree　is　presented.　Results　show　that　the　improved　method　generates　less　than　half　of　mesh　nodes　with　only　one　step　of　mesh　refinement　comparing　to　Elena　Zhelezina＇s　method.