Focusing on the problem that the echo state network is easily influenced by outliers, in this paper we propose a robust model based on the Laplace prior distribution. This is achieved by replacing the Gaussian distribution with the Laplace distribution as the prior of the model output, the Laplace prior is less sensitive to the outliers and can enhance the capbility of the model to restrict outliers. Furthermoer, to solve the problem arising from the introduction of the Laplace distribution, which makes the solving process of the method difficlut, the bound optimization algorithm is employed and a suitable surrogate function is established. Based on the bound optimization algorithm, the Laplace prior can be equivalently transformed into the form of Gaussian prior, which is easily computed, and it can also be use to estimate the model parameters adaptively. Simulation results illustrate that the proposed method can be robust when outliers exist, while remaining acceptable prediction accuracy.