Chaotic systems have important research significance in circuit, secure communication, encryption and decryption. The traditional statistical time series prediction methods are challenging in dealing with the chaotic systems because the chaotic systems are very sensitive to the initial values. Echo state network is a special cyclic neural network, and has advantages in the dynamics and control of complex dynamic systems. The classical echo state network places all samples in the same importance, however in practical problems, the importance of the samples are often different. This paper proposes the attention mechanism echo state network by combining the echo state network and the attention machine to reflect the differences and interactions between samples. The prediction results on chaotic systems show that the prediction performance of the echo state network with attention mechanism is better than that of the classical methods.