For the case of using small sample data to predict the annual runoff which caused unsatisfactory results,and the case of trying to deal with asymmetric and non-normal data.The thought of information diffusion and fuzzy mapping were introduced in this paper.At the same time,we tried to set up a new diffusion interpolation model by using genetic algorithm to improve the theory of optimal window width.The model achieved probability interpolation of limited data point information to its neighboring regions point by improving the theory of optimal window width based on genetic algorithm.In order to verify the practicability of the model,this paper took Li Jin hydrological station of the Yellow River as an example,and its runoff data from 1942 to 2011 were interpolated and prediction experiments were conducted.After comparing with the normal diffusion interpolation model,the following conclusions can be drawn:(1) In the interpolation and prediction of the runoff data in some non symmetric and non normal data,the results of interpolation is approximate to the actual and the predictive value which can well simulate the waveform changes of actual runoff series,especially accurate in both wet years (such as 2007) and dry years (such as 2009);(2) The average relative error of long-term forecasts (usually 10 years) is only 11.59%,which met the requirements and achieved greater improvement when compared with traditional information diffusion method whose average relative error is 55.23%;(3) Finally,the prediction experiment of annual runoff of two hydrologic stations in the Yellow River Basin(Huayuankou and Lanzhou) and three hydrologic stations in the Yangtze River Basin(Zhutuo,Yichang and Datong) and the interpolation experiment of sea surface temperature data as a complement,which can verify the effectiveness of the proposed method and the general applicability.Owing to the transformation from sample points into fuzzy sets,the new algorithm can partially make up for the information gaps due to incomplete data.It can not only be applicable to the estimation and prediction of annual runoff of hydrological stations with different geographical positions,different underlying surfaces and different catchment areas,but also can be extended to the interpolation prediction field of sparse data,especially in the field of atmosphere and ocean.This new interpolation model which is proposed by this paper is intended to provide a reference for objective analysis and long-term forecasts of actual hydrological data.