Abstract: In this paper a novel neural network architecture is proposed for predicting time series The new neural network is called product unit neural network with finite impulse response synapses （PUNN with FIR）, which has simple structure and power information storage capacity Application considered is a chaotic time series with a small sample set Experiment results of single step and multi step prediction are obtained by PUNNs with FIR, standard PUNNs and fuzzy neural networks respectively The results show that performance of PUNNs with FIR is superior to that of standard PUNNs and fuzzy neural networks The work demonstrates that the PUNN with FIR is an efficient method for predicting time series, especially in small training sample set situations