An increasing number of floating offshore wind turbines are planned and designed these days due to their vast potential in massive generation of clean energy from ocean wind. In the present study, a numerical prediction tool has been developed for the fully coupled dynamic analysis of an offshore floating wind turbine system in time domain including blade-rotor dynamics and control, mooring dynamics, and platform motions. In the new computer program, the dynamic coupling between the rotating blades and the floater is considered in addition to the mooring-floater dynamic coupling so that the influence of rotor dynamics on the hull-mooring performance and vice versa can be assessed. Mono-column mini TLPs with 1.5MW units for two different water depths, 80m and 200m, are selected as an example. The TLP becomes stiffer both in horizontal- and vertical-plane modes as water depth decreases. As a result, wave-frequency motions and the resulting tendon tensions tend to increase in the 80-m case. However, the coupling effects with rotors are decreased in the shallower depth case. When compared with the uncoupled analysis, we can observe more pronounced rotor-dynamics effects at high frequencies in the coupled simulations, which may appreciably influence fatigue life in the case of larger blades. The developed technology and numerical tool are readily applicable to the design of new offshore floating wind farms in irregular waves, dynamic winds, and steady currents.