To address the issues of traditional mooring lines, such as high self-weight, low strength, and poor durability, Carbon-Fiber-Reinforced Polymer (CFRP) was investigated as a material for mooring lines of offshore floating wind turbines, aiming to achieve high performance, lightweight design, and long service life for mooring systems. Based on a “chain–cable–chain” configuration, a CFRP mooring line design is proposed in this study. Taking a 5 MW offshore floating wind turbine as the research object, the dynamic performance of offshore floating wind turbines with steel chains, steel cables, polyester ropes, and CFRP mooring lines under combined wind, wave, and current loads was compared and analyzed to demonstrate the feasibility of applying CFRP mooring lines by combining the potential flow theory and the rigid–flexible coupling multi-body model. The research results indicate that, compared to traditional mooring systems such as steel chains, steel cables, and polyester ropes, (1) under static water, the CFRP mooring system exhibits a larger static water free decay response and longer free decay duration; (2) under operating sea conditions, the motion response and mooring tension of the offshore floating wind turbine with CFRP mooring lines are smaller than those with steel cables and steel chains but greater than those with polyester ropes; and (3) under extreme sea conditions, the motion responses of the offshore floating wind turbine with CFRP mooring lines are smaller than those with steel wire ropes and steel chains but close to the displacement responses of the polyester rope system, while the increase in mooring tension is relatively moderate and the safety factor is the highest.