A direct multi-step prediction model based on chaotic and second order diagonal recurrent neural network with
two recurrent weights in hidden layer is proposed. A generalized dynamic back-propagation(DBP) algorithm is applied to
training, and the convergence of DBP is derived. Simulation results show that, direct multi-step prediction does not depend
on the results of single-step prediction, and the proposed network can make a rapid and accurate prediction of the ship rolling
time series, and provides more prediction accuracy and more prediction time by comparing to single-step prediction.