Abstract: In this paper, we study the convergence property of the projection pursuit learning network （PPLN）, which is used to approximate to multivariate nonlinear autoregression. The authors first prove that PPLN can approximate to multivariate nonlinear autoregreesion at any given precision in L^k space that k is integer, k≥ 1. The learning strategy and calculation procedures of PPLN, which are used to establish the model and forecast the subsequent behavior of multivariate nonlinear time series X_t, are also presented. We derive the consistency results and conclude from simulation and real data analysis that the new method has better convergence property and predictive potential than backpropagation learning network （BPLN）.