The autonomous anti-sway control of the ship-mounted crane systems is a tough issue due to the under-actuated characteristic, strong coupling and base excitation. Furthermore, the ship-mounted crane systems are also suffering from unknown dynamics and frictions etc. In some conditions, the ship-mounted cranes may exhibit spherical pendulum effects. These factors make the control problem even more challenging. To solve the above problems, this paper designed a Radical Basis Function Neural Network (RBFNN) based feedback control method for a 5-DOF ship-mounted rotary crane. Specially, the adaptive RBFNN is established to approximate the unknown dynamics online. After that, eschewing any simplification of the dynamic model, a feedback anti-sway control is designed to ensure the cargo could reach to desired position and dampening the payload spherical swing simultaneously. The closed-loop stability is analyzed and the effectiveness of the control method is validated via simulation experiment results.