The control objectives in this paper are to move the load of a container crane to its target position and to suppress the transverse vibration of the load. Owing to the fact that the load is hoisted up and down, the crane is modeled as an axially moving string system. The dynamics of the moving string are derived using Hamilton’s principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, where the Lyapunov function candidate takes the form of the total mechanical energy of the system. The boundary control law utilizes the hoisting speed as well as the sway angle of the rope at the gantry side. Through experiment, the effectiveness of the proposed control law is demonstrated particularly in the lift-up process of the load.