Aiming at the problem of underactuated shipborne jib cranes subjected to persistent uncertain upper-bound disturbances, an adaptive radial basis function neural network (ARBNN) hierarchical sliding mode control (HSMC) method (called ARBFNN-HSMC method) is proposed. The dynamical model of the ship-crane-payload complex system affected by sustained sea waves is established using the Lagrangian method and converted into the standard form of an underactuated system. HSMC method is employed to design the control law, compensating for system parameter perturbations. ARBFNN is used to approximate and compensate for disturbances with uncertain upper bounds caused by external nonlinear disturbances. The asymptotic stability of the system is proven using the Lyapunov function. Simulation results demonstrate that the proposed method exhibits strong robustness under persistent unknown disturbances and effectively achieves the dual objectives of payload positioning and oscillation elimination.