In this paper, a robust vibration control scheme of the axially moving steel strip in the zinc galvanizing line is considered. The boundary control force is applied to the strip through the two touch rolls connected to a hydraulic actuator. The mathematical model of the system, which consists of a partial differential equation describing the dynamics of the traveling steel strip and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton’s principle for the systems with changing mass. The total mechanical energy of the system is considered as a Lyapunov function candidate. For vibration suppression purpose, a robust boundary feedback control law is designed. The asymptotic stability of the closed loop system is verified through the Lyapunov analysis and the semigroup theory.