In this paper, a neural network-based robust anti-sway control is proposed for a crane system transporting an underwater object. A dynamic model of the crane system is developed by incorporating hoisting dynamics, hydrodynamic forces, and external disturbances. Considering the various uncertain factors that interfere with accurate payload positioning in the water, neural networks are designed to compensate for unknown parameters and unmodeled dynamics in the formulated problem. The neural network-based estimators are embedded in the anti-sway control algorithm, which improves the control performance against uncertainties. A sliding mode control with an exponential reaching law is developed to suppress the sway motions during underwater transportation. The asymptotic stability of the sliding manifold is proved via Lyapunov analysis. The embedded estimator prevents the conservative gain selection of the sliding mode control, thus reducing the chattering phenomena. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.