As　there　may　be　complex　solutions　in　the　traditional　approximate　non-homogeneous　GM(1,1)　model,　this　paper　proposes　the　recursive　solution　to　unbiased　GM(1,1)　model,　which　can　reduce　the　errors　from　the　differential　equation　to　differential　equation.　And　its　predictive　formulas　are　given　under　differentinital　conditions　with　the　recursive　method.　On　this　basis,　by　appling　the　recurisive　formulas　to　time　series　piecewise　representation,　the　method　of　time　series　piecewise　representation　based　on　the　new　model　is　proposed.　The　results　show　that　the　recursive　model　has　higer　fitting　precision,　and　also　verify　the　effectiveness　and　the　practicability　of　the　representation　method　of　time　series　based　on　the　grey　forecasting　model.　©　2015,　Northeast　University.　All　right　reserved.