This paper considers a control system for a crane that reduces pendulation of suspended loads in offshore lifting operations. The modelling of the ship crane is studied and an anti-pendulation arm is designed and proposed. Two different types of models are derived, one based on torque and one kinematic. For the torque model, Lyapunov analysis and non-linear control design is applied on the vertical plane. Linear control design techniques for the linearized kinematic model are applied in both vertical and horizontal planes. These techniques are based on linear quadratic Gaussian (LQG) and generalized predictive control (GPC). The advantage for the linear control designs is the explicit use of the vessel dynamics and sea wave disturbances in the control design that considerably improves the controlled pendulation of the crane. Design issues, simulation results and comparison studies are considered.