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.