The problem of sigular solution in echo state network(ESN) learning algorithm is existed, which is easy to cause
ill issue. Especially when training samples are less than the dimenssions of the output, the solution of the ESN must be
singular. Therefore, Levenberg Marquardt(LM) algorithm is used to learn ESN instead of linear regression method, which
can effectively control the amplitude of the output weight result in improved predictive performance. The presented model
is tested on the Lorenz time series and applied to some real life time series such as Dalian monthly average temprture time
series. Actual simulation results show that the predictive model has higher predictive accuracy, and is of great practicality
and effectiveness.