Floating raft vibration isolation systems have been plagued by multi-frequency vibration and vibration suppression for the low-frequency range. In this paper, the floating raft vibration control strategy using multiple distributed nonlinear energy sinks (NESs) is proposed for the first time. In the modeling, three kinds of distributed NESs, namely, being connected to the power units only, to the raft and elastic base only, and to the entire substructure of the system, are considered. Based on this five-degree-of-freedom dynamic model, the natural frequencies and modes are analyzed. The approximate analytical analysis of the nonlinear model is carried out, and the correctness of the approximate solution is verified numerically. The vibration reduction efficiency of the three NES distribution models is demonstrated. The results show that the distributed NESs can effectively control the vibration of the floating raft system for all modes. The vibration problem of the floating raft system for the low-frequency range is perfectly solved. Furthermore, with a small additional weight ratio, different NES distribution models can be used to achieve the vibration damping of the floating raft system for low-order or high-order modes. In conclusion, this paper provides a novel and efficient control strategy for floating raft vibration.