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To overcome the contradiction of the traditional grey first order accumulate with the new information priority principle, this paper establish the new grey fractional order accumulate, which is proposed to better reflect the priority of the new information. Based on this, This paper establish the fractional order grey direct model based on the principle of new information priority, which is proposed to improve the prediction precision. The results of practical numerical examples demonstrate that this new method has a good predication performance for small data set forecasting. This research also provides a new model for the less data forecasting.