A methodology for the design and optimization of a composite wind turbine tower for use on a floating offshore platform is presented. A composite turbine tower on a floating offshore platform not only has the potential to reduce maintenance and upkeep costs associated with the use of steel offshore but also has potential to reduce the tower mass and subsequently the support platform mass. The optimization problem is formulated to obtain a turbine tower that meets all strength and serviceability criteria and minimizes the tower mass. The optimization and design process link a number of dynamic analyses and finite element routines using a genetic algorithm. This work documents the optimization and design software and illustrates its use in various case studies for a 6 MW floating wind turbine system. Case studies include the optimization of a steel tower as a comparison to a composite material tower and the use of a cored, sandwich panel composite tower versus a solid composite tower. The results demonstrate that significant reductions in the tower mass are likely when comparing a steel tower with a composite tower. Also demonstrated for the platform and turbine configuration considered in this work is that the minimum mass tower design is driven towards a solid shell composite configuration, rather than a sandwich panel tower shell, in the face of reasonable design constraints.