To improving the fitting and prediction effects of the non-equal interval GM(1,1) model, based on analyzing the main factors of the error source of this model, an improved non-equal interval GM(1,1) model based on grey derivative and accumulating generation is proposed in this paper. Considering that the accumulating algorithm affects the exponential strength of the generated sequence and the geometric sequence implies the exponential form, a new algorithm for the accumulating generation of non-equal interval sequences is proposed, and a new grey derivative optimization method and parameter estimation method are proposed based on the new accumulating algorithm. Additionally, this paper infers to the accumulating algorithm of the traditional non-equidistant GM (1,1) model is an approximation of the new accumulating method in the case of a smaller development coefficient. The findings show that the model under the new parameter estimation method has several properties, including multiply transformation, does not change the fitting prediction and the white index rate coincidence. Finally, we verify the validity and practicability of the improved non-equal interval GM(1,1) model by examples.