In this paper a generalized discrete GM(1,1) model with optimized initial value (GDGM) is put forwarded to provide the solution steps in order to solve the grey prediction modeling of non-equidistance series. This method can be utilized in solving the non-equidistance grey prediction problem with integral interval or digital interval. The GDGM model has no strict data requirement to the raw data sequence. It expands the application range of traditional GM(1,1) model and non-equidistance grey prediction model in many aspects and has higher prediction accuracy. The numerical results indicate GDGM model can perfectly simulate non-equidistance exponential series.
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