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This paper analyzes the dynamics of an offshore boom crane and proposes a high-performance nonlinear controller to drive the system states to track some constructed trajectories. Specifically, by employing Lagrange's method in an attached frame, a dynamic model is obtained for the offshore crane system consisting of the boom and a payload, with specific emphasis on the effect of the vessel's motion on the payload swing. Based on the model, a novel nonlinear control law is designed for the underactuated boom crane, which makes the system states track some planned trajectories successfully, even in the presence of persistent disturbance in harsh sea conditions. The stability of the designed closed-loop system is proven by Lyapunov techniques. Simulation and experimental results are included to demonstrate that the proposed control method significantly reduces the impact of the disturbance in harsh sea conditions.