A new method to improve prediction precision of GM(l,1) model with unequal time interval is presented. The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately exponential function distribution. To simplify the process of parametric estimation, an approximate value is taken for the multiplied parameter. Then the estimators of coefficient of development and grey action quantity can be derived. At the same time, the principle of the new informarion priority is also considered. We take the last item of the first-order accumulated generation operator (1-AGO) on raw data sequence as the initial condition in the time response function.Then the new information can be taken full advantage of through the improved initial condition. Some properties of this new model are also discussed. The presented method is actually a combination of improvement of grey derivativa and improvement of the initial condition. The results of an example indicate that the proposed method can improve predictJon precision prominently.