In this study, an adaptive boundary control is presented for vibration suppression of an axially moving belt system. First, the infinite-dimensional model of the belt system including the dynamics of high acceleration/deceleration and distributed disturbance is derived by utilising the extended Hamilton's principle. Subsequently, by using Lyapunov's synthesis method and an adaptive technique, an adaptive boundary control is developed to suppress the belt's vibration and compensate for the system parametric uncertainties. With the proposed control, the stability of the closed-loop system and the uniform boundedness of all closed-loop signals are both ensured. Besides, the S-curve acceleration/deceleration method is adopted to plan the belt's axial speed and the disturbance observer is used to mitigate the effects of unknown boundary disturbance. Finally, the control performance of the closed-loop system is successfully demonstrated through simulations.