Objective: Offshore wind energy is considered an attractive solution for power generation and environmental conservation. Floating offshore wind turbines (FOWTs) are feasible systems when the water depth exceeds 60 m, where the total cost for the bottom-fixed wind turbine increases. FOWTs usually keep position by using mooring systems, which provide up to 80% of the total damping in surge under certain circumstances. Furthermore, the mooring system accounts for approximately 20%—30% of the overall cost of an FOWT. Since the mooring system performance significantly affects the operational safety, power generation efficiency, and economic cost of an FOWT, it is necessary to select an appropriate mooring system based on engineering standards and requirements. The analysis and optimal design for the mooring system of a floating wind turbine involve many factors and variables and are usually conducted by trial-and-error method, requiring amounts of computational resources and time. Methods: This study proposes a multiobjective optimization method for the mooring system of a floating wind turbine, considering station-keeping ability, safety performance, and economic performance. Then, the intelligent optimization design program for this problem is developed based on the genetic algorithm and quasistatic mooring analysis code. On the basis of the aforementioned methods, the mooring system of a 15-MW floating wind turbine that was designed for a water depth of 50 m in the South China Sea is redesigned and optimized. The motion responses, safety performance, and cost of the original and optimized designs are compared and analyzed under operating, extreme, and breaking conditions. Results: The results show the following: First, the intelligent optimization program of the mooring system effectively achieves the optimization objectives and meets the requirements, as well as solves the complex multiobjective and multivariable problems in the mooring design process, which can significantly save the time and computing resources. Second, considering the construction and installation costs of the mooring line and anchor, the economic cost of the optimized solution is 17% lower than that of the original one, demonstrating significant economic improvement. Moreover, the damping of surge and sway of the optimized design is 69.30% and 21.43% greater than that of the original design, respectively, which is beneficial for reducing the horizontal motion of the floating wind turbine and mooring tension amplitude. Finally, with the optimized mooring system, the pitch maximum of the floating wind turbine at rated wind speed is reduced by 10.28%, which could be beneficial for improving the power generation efficiency. Both the optimized and original mooring systems meet the design requirements, and the horizontal motion amplitude is in good agreement under extreme conditions. In addition, under breaking conditions, the amplitude of the surge and the pitch motion of the floating wind turbine with the optimized mooring system are obviously reduced, and the safety factor of the mooring line is increased by 9.61%, which significantly reduces the risk of dragging anchor and improves the performance. Conclusions: Based on the aforementioned research, the feasibility and superiority of the intelligent optimization mooring design method and program are verified. This study could provide an engineering approach for mooring optimal design of the FOWT.