A modified free-wake vortex ring model is proposed to compute the dynamics of a floating horizontal-axis wind turbine. The model is divided into two parts. The near wake model uses a blade bound vortex model and trailed vortex model, which is developed based on vortex filament method. By contrast, the far wake model is based on the vortex ring method. This is a good compromise between accuracy and computational cost. In this work, the model is used to assess the influence of floating platform motions on the performance of a horizontal-axis wind turbine rotor. The results are validated on the 5MW NREL rotor and compared with other vortex models for the same rotor subjected to different platform motions. It was found that the result from the proposed method are more reliable than the results from BEM theory especially at small angles of attack in the region of low wind speeds, on the one hand, and high wind speeds with blade pitch motions, on the other hand.