As onshore wind energy has depleted, the utilization of offshore wind energy has gradually played an important role in globally meeting growing green energy demands. However, the cost of energy (COE) for offshore wind energy is very high compared to the onshore one. To minimize the COE, implementing optimal design of offshore turbines is an effective way, but the relevant studies are lacking. This study proposes a method to minimize the COE of offshore wind turbines, in which two design parameters, including the rated wind speed and rotor radius are optimally designed. Through this study, the relation among the COE and the two design parameters is explored. To this end, based on the power-coefficient power curve model, the annual energy production (AEP) model is designed as a function of the rated wind speed and the Weibull distribution parameters. On the other hand, the detailed cost model of offshore turbines developed by the National Renewable Energy Laboratory is formulated as a function of the rated wind speed and the rotor radius. Then, the COE is formulated as the ratio of the total cost and the AEP. Following that, an iterative method is proposed to search the minimal COE which corresponds to the optimal rated wind speed and rotor radius. Finally, the proposed method has been applied to the wind classes of USA, and some useful findings have been obtained.