This paper present a neural predictive controller (NPC) based on improved quasi-ARX neural network (IQARXNN) for nonlinear dynamical systems. The IQARXNN is used as a model identifier with switching algorithm and switching stability analysis. The primary controller is designed based on a modified Elman neural network (MENN) controller using back-propagation (BP) learning algorithm with modified particle swarm optimization (MPSO) to adjust the learning rates in the BP process to improve the learning capability. The adaptive learning rates of the controller are investigated via Lyapunov stability theorem, which are respectively used to guarantee the convergences of the predictive controller. Performance of the proposed MENN controller with MPSO is verified by simulation results to show the effectiveness of the proposed method both on stability and accuracy.