The increased interest in the offshore wind resource in both industry and academic and the extension of the wind field where offshore wind turbine can be deployed has stimulated quite a number of offshore wind turbines concepts. This thesis presents a design of mono-column platform supported for 5 MW baseline wind turbine developed by the National Renewable Energy Laboratory (NREL), with a single tether anchored to the seabed. The design, based on the pioneer concept SWAY, results from parametric optimized design processes which account for important design considerations in the static and dynamic view, such as the stability, natural frequency, performance requirements as well as the economic feasibility. Fully coupled aero-hydro-servo-elastic model is established in the time-domain simulation tool FAST (Fatigue, Aerodynamics, Structures, and Turbulence) with the hydrodynamic coefficients from HydroGen, an indoor program providing same outputs as the commercial software WAMIT. The optimized model is verified by imitating the frequency-domain approach in FAST and thus comparing the results with the frequency-domain calculations. A number of simulations with various wind and wave conditions are run to explore the effect of wind speed and wave significant height in various water depths. By modifying the optimized model to a downwind turbine with the nacelle rigidly mounted on the tower and the single tether connected to the platform by a subsea swivel, the modified models are more closed to the original SWAY-concept wind turbine. These models are compared based on the platform motion, tether tension, displacement, nacelle velocity and acceleration, resonant behavior as well as the damping of the coupled systems. The results of these comparisons prove the advantage of the modified model in performance. The modified model has also clarified itself a good candidate for deep water deployment.