To suppress structure vibration and avoid control spillover, a boundary controller is proposed for active vibration control of an axially moving system with high ac-/deceleration. The proposed boundary controller, which is based on the infinite-dimensional model of the axially moving system derived from generalized Hamilton’s principle, employs the boundary technique and Lyapunov’s direct method to reduce the axially moving system vibration. With the proposed boundary control method，the control spillover is avoided, and control system stability and uniform boundary are both achieved under external disturbances．Simulation results indicate that the proposed boundary control method effectively suppresses the vibration of the axially moving structure．