A dynamic model for a tension-leg platform (TLP) floating offshore wind turbine is proposed. The model includes three-dimensional wind and wave loads and the associated structural response. The total system is formulated using 17 degrees of freedom (DOF), 6 for the platform motions and 11 for the wind turbine. Three-dimensional hydrodynamic loads have been formulated using a frequency- and direction-dependent spectrum. While wave loads are computed from the wave kinematics using Morison's equation, the aerodynamic loads are modeled by means of unsteady blade-element-momentum (BEM) theory, including Glauert correction for high values of the axial induction factor, dynamic stall, dynamic wake, and dynamic yaw. The aerodynamic model takes into account the wind shear and turbulence effects. For a representative geographical location, platform responses are obtained for a set of wind and wave climatic conditions. The platform responses show an influence from the aerodynamic loads, most clearly through quasi-steady mean surge and pitch responses associated with the mean wind. Further, the aerodynamic loads show an influence from the platform motion through a fluctuating rotor load contribution, which is a consequence of the wave-induced rotor dynamics. Loads and coupled responses are predicted for a set of load cases with different wave headings. Further, an advanced aero-elastic code, Flex5, is extended for the TLP wind turbine configuration and the response comparison with the simpler model shows a generally good agreement, except for the yaw motion. This deviation is found to be a result of the missing lateral tower flexibility in the simpler model.