In this paper a sieve bootstrap scheme, the Neural Network Sieve bootstrap, for nonlinear time series is proposed. The approach, which is non parametric in its spirit, does not have the problems of other nonparametric bootstrap techniques such as the blockwise schemes. The procedure performs similarly to the AR-Sieve bootstrap for linear processes while it outperforms the AR-Sieve and the moving block bootstrap for nonlinear processes, both in terms of bias and variability.