This paper proposes an adaptive feedback control for an offshore boom crane. The offshore crane is a typical nonlinear under-actuated mechanical system, which has three independent control input (i.e., the boom luffing and rotating control torques and the cable length control force) and more than four degrees of freedom (DOFs). These characteristics make the control of an offshore boom crane a difficult issue. The offshore crane is suffering from the persistent ship movement induced disturbances which make the control problem more challenging. Furthermore, in practice, the offshore crane would hoist payloads with different mass and the payload mass is usually unknown. Such that, it is more suitable to design robust anti-swing control methods which do not need the payload mass information. In this paper, the adaptive method is used to approximate the payload mass online and then an energy-based feedback anti-swing control method is proposed to regulate the payload to desired positions and suppress the residual swing. The closed-loop stability is analyzed by using the Lyapunov theory. The effectiveness of the proposed control method is verified via the simulation results.