Accurately obtaining channel state information (CSI) in wireless systems is significant but challenging. This paper focuses the technique of machine-learning-based channel estimation. In particular, a jointly optimized echo state network (JOESN) is proposed to form a concept of the CSI prediction which is made up of two interacting aspects of output weight regularization and initial parameter optimization. First, in order to enhance noise robustness, a sparse regression based on L2 regularization is employed to finely learn the output weights of ESN. Second, vital reservoir parameters (i.e., global scaling factor, reservoir size, scaling coefficient and sparsity degree) are learned by a linear-weighted particle swarm optimization (LW-PSO) for further improve the prediction accuracy and reliability. The experiments about computational complexity and three evaluating metrics are carried out on two chaotic benchmarks and one real-world dataset. The analyzed results indicate that the JOESN performs promisingly on multivariate chaotic time series prediction.