The erection process of military bridge vehicles was simplified into an axially moving cantilever beam system that is continuously stimulated by external forces. The Lagrange method was used to derive the time-varying dynamics equation of the system, and the Galerkin method with power series function as trial function was used to solve the discrete equation. At the same time, the influence of erection speed on the vibration of the bridge was analyzed, and suitable erection speed strategy was given. Finally, model predictive control based on a Newmark method was proposed to actively control the vibration of the bridge. The influence of relevant parameters in the control strategy on vibration control was discussed and a suitable value range was given. The comparison of the results shows that model predictive control based on the Newmark method has obvious control effect and good robustness. © 2021, Editorial Office of Journal of Vibration and Shock. All right reserved.