To avoid singular problem and improve the performance of neural network, a weight initialization method for echo state network(WIESN) is proposed. With Cauchy inequality and linear algebra, the range of optimal initial weights, which is related to input dimension, reservoir dimension, input variables and reservoir state, is determined. The proposed method ensures that the outputs of neurons are in the active region. Simulation results show that the accuracy and training time of the proposed method is better than learning with random initialization. In addition, the time for weight initialization process is negligible comparing with the training process.