In recent years, offshore wind energy has experienced a huge development. Floating wind turbines may become competitive for water depth larger than 50m. However, high cost is still the main challenge for the offshore wind industry. Floating offshore designs provides the possibility to carry large wind turbines to reduce the cost per MWh. In this thesis, a pontoon-type semi-submersible platform has been designed to support the DTU 10MW reference wind turbine. The initial design is made though upscaling of an existing 5MW semi-submersible platform design. The design is then checked against buoyancy, stability, hydrodynamic and strength criteria. In addition a spread catenary mooring system has been designed based on the catenary theory. Further tests show that clump weight might be needed to balance the strength and stiffness of the mooring lines. Floating wind turbine models with different levels of complexity have been established and studied through the thesis. In addition, viscous drag force and second order wave force have been implemented. Finally the SIMO-RIFLEX-AeroDyn model is established, and extensive numerical tests have been performed to check the model. The modelling of blades, hub, nacelle and shaft has been found to be difficult and will result in some difficulties in eigenfrequency prediction of the wind turbine. It is also found that the blade pitch controller can excite large platform pitch resonant motion at above rated wind speeds, which could be possibly solved by reducing the PI gains of the controller. Finally, time domain coupled dynamic analysis of the floating wind turbine system is performed by the SIMO-RIFLEX-AeroDyn code. Characteristic responses of the semi-submersible floating wind turbine are studied and compared to those of the land-based wind turbine. It is found that platform motions have limited influence on the aerodynamic performance of the wind turbine. Besides, operating at rated wind speed is found to produce the largest blade and tower bending moments for both land-based and floating wind turbines. For the floating wind turbine, resonant surge and pitch motions could be excited by turbulent wind under operational conditions which will dominate the response. Second order wave force has some influences on the surge and pitch resonant responses, but these influences are small comparing to those of turbulent wind. However, second order wave force could be important for the study of heave motion, which is wave force dominated even under turbulent wind conditions.