To maintain the stable suspension of high-speed maglev vehicles, a predictive control algorithm based on neural networks is proposed. Initially, the vehicle dynamic response prediction model is built using the long short-term memory neural network considering its’ time-varying and nonlinear characteristics. This predictive model achieves precise online prediction of the electromagnetic suspension gap. Then, the prediction model is utilized to construct the predictive control algorithm. Finally, the effectiveness of this algorithm is verified by simulations and experiments. The results demonstrate that the prediction model can accurately and continuously predict the maglev vehicle’s future dynamic responses. Predictive control algorithms can predict fluctuations in the suspension gap before they occur and provide feedforward compensation. Experimental results prove that the predictive control algorithm can effectively suppress electromagnet fluctuations to achieve better stable suspension.