In order to improve the accuracy of yield prediction, we attempted to combine the power spectrum analysis(BP filter) in economics and the Fourier model in statistics, by using BP filter to choose the cycle, which had a great impact on the climate yield fluctuation, and established Fourier model to predict the climatic yield. At the same time, by using polynomial to predict the trend yield and the lag model to correct the residual. Grain yield data from 1961 to 2000 was taken as training data, by using three methods, Fourier method and polynomial lag method, BP neural network and grey model to construct the equations, and grain yield from 2001 to 2012 was used to test the three models. The three methods were compared by the fitting results. The results showed that the model was significant and the relative errors were all less than 5%. The predicted grain yields according to this model were at 6018.6-6466.7kg?ha~(-1) from 2013 to 2017. Meanwhile, the relative errors by BPNN were small, but the model could not be explained intuitively. The relative errors by the grey model reached up to 35%, it existed large differences with the actual yield. The results indicated that, in terms of predicting the grain yield, the Fourier model based on BP filter and the polynomial lag model had higher prediction accuracy and was more intuitive, which could not only predict the future grain yield, but also predict the impact of the future climate change on the grain yield.