Abstract: The convergence property of the projection pursuit learning network （PPLN） that is used to approximate to non-linear autoregression is studied in this paper. The authros prove that PPLN can approximate to non-linear autoregression at any given precision in L^k space, where k is integer. The learning strategy and calculative procedures of PPLN’s, which are used to establish the models of non-linear time series X_t and forecast the subsequent behavior of X_t, are also presented. Using PPLN, tile Wolfer sunspont number（1749-1894）, Canada lynx data（1821-1924） and Xi’an data（0-360） are fitted. Furthermore, the predictors for the above three kinds of data are also presented, respectively. Finally, we compare the performance the projection pursuit learning network not only with that of baekpropagation learning （BPLN） but also with that of the threshold model. It is shown that the projection pursuit learning networks perform well and compare favorably to BPLN and the threshold model.