Since the support structure of an offshore wind turbine has to withstand severe environmental loads such as wind, wave, and seismic loads during its entire service life, the need for a robust and reliable design increases, along with the need for a cost effective design. In addition, a robust and reliable support structure contributes to the high availability of a wind turbine and low maintenance costs. From this point of view, this paper presents a design process that includes design optimization and reliability analysis. First, the jacket structure of the NREL 5-MW offshore wind turbine is optimized to minimize the weight and stresses, while satisfying the design requirements. Second, the reliability of the optimum design is evaluated and compared with that of the initial design. Although the present study results in a new optimum shape for a jacket support structure with reduced weight and increased reliability, the authors suggest that the optimum design has to be accompanied by a reliability analysis during the design process, as well as reliability based design optimization if needed.