A floating nuclear power plant is essentially a ship equipped with a small mobile reactor. The loading and unloading operations are carried out by a gantry crane on board. The ship’s sway presents a significant challenge to lifting operations. This paper proposes a multi-directional, rope-driven parallel mechanism along with an anti-sway strategy. During crane operation, the anti-sway drive system ensures that the rope remains in a taut state at all time. On one hand, the rope coordinates with the movement of the crane trolley and the lifting of the winch through low-frequency retraction. On the other hand, the system actively controls the swaying of the suspended object through high-frequency retraction. A rigid-flexible coupling dynamic model was established to represent the series-parallel interaction among the ship, the crane, the sway compensation device, the rope, and the suspended object. The control variable method was used to investigate the influence of mass and wave excitation period. To stabilize the suspended object relative to the target point, an anti-sway strategy based on hook position adjustment was also developed. A working condition test was conducted to validate this strategy. After applying anti-sway control based on hook position adjustment, the sway amplitude of the suspended weight significantly decreased.