In this paper, we proposed a new echo state network (ESN) model, namely echo state network based on memristor (memristor-ESN). It improve the memory function of the reservoir and the prediction performance of the ESN. In the memristor-ESN, memristor is used to replace the synapses between neurons in the reservoir of echo state network. In the prediction of chaotic time series, we compare the classical echo state network with the echo state network based on memristor. Simulations are conducted to verify the prediction accuracy and prediction performance of the memristor-ESN.