Offshore floating wind turbines may undergo swaying motions, resulting in significant changes in the wake wind field characteristics of the wind turbine, which can seriously affect the applicability and accuracy of existing wake models. This paper systematically investigates the turbulent wake flows of floating wind turbine with swaying motion based on an improved actuator disk method (ADM). The improved ADM is introduced to reproduce the wake flows of wind turbines, and the characteristics of the turbulent wind fields (i.e., mean wind velocity, turbulence intensity and Reynolds stress) are verified by wind tunnel tests. Furthermore, the wind fields of a floating wind turbine with different swaying amplitudes under turbulent atmospheric boundary layer are simulated, and the mean wind fields and turbulent statistics are analyzed. The performance of various existing wake models (i.e., Jensen model, modified Jensen model and Gaussian model) are compared, and a Gaussian-Shear wake model is proposed for floating wind turbines, which can account for non-uniform inflow and accommodate different swaying amplitudes. The results indicate that the proposed Gaussian-Shear wake model outperforms the other three models in describing the wake flows of floating wind turbines with swaying motions, which can be used for layout optimization and yaw control of offshore floating wind turbines.