Echo state network can effectively capture dynamic features in time series data. Within the architecture of the echo state network, its performance is influenced by the selection and adjustment of network structural parameters, thus classic echo state networks have unstable predictions. In order to optimize the performance of the echo state network, improve the stability and accuracy of prediction, this paper introduces Chebyshev mapping to replace the random initialization of the input matrix. Chebyshev mapping can enrich the nonlinear states inside the reserve pool, capture more information inside the reserve pool, and introduce error functions in the reserve pool state update formula for regulation. Combined with genetic algorithms, the echo state network has the ability to update in reverse. Through parameter optimization and adjustment, the prediction accuracy is further improved. In summary, this article introduces Chebyshev mapping, error function, and combines genetic algorithm to propose an improved echo state network model (CM_Err_ESN), and further verifies the prediction on the Mackeyglass dataset and Wind Turbine Scada dataset. The experimental results show that compared with the classic echo state network model (ESN), ESN model with Chebyshev mapping (CM_ESN) and ESN model with error function (Err_ESN), the proposed CM_Err_ESN model achieves better prediction performance.