This paper describes the extension of a well proven state-of-the-art simulation tool for coupled floating structures to accommodate offshore wind turbine applications, both floating and fixed. All structural parts, i.e. rotor blades, hub, nacelle, tower, vessel and mooring system, are included in the finite element model of the complete system. The aerodynamic formulation is based on the blade element momentum theory. A control algorithm is used for regulation of blade pitch angle and electrical torque. The system response is calculated by nonlinear time domain analysis. This approach ensures dynamic equilibrium every time step and gives a proper time domain interaction between the blade dynamics, the mooring dynamics and the tower motions. The developed computer code provides a tool for efficient analysis of motions, support forces and power generation potential, as influenced by waves, wind, and current. Some key results from simulations with wind and wave loading are presented in the paper. The results are compared with results obtained with a rigid blade model and quasi-static model of the anchor lines. The modelled wind turbine is the NREL offshore 5-MW baseline wind turbine, specifications of which are publicly available. In the accompanying paper, Global Analysis of a Floating Wind Turbine Using an Aero-Hydro-Elastic Numerical Model. Part 2: Benchmark Study, results from the new analysis tool are benchmarked against results from other analysis tools.