Understanding the unsteady characteristics of the mid-to-far wake and comprehension of the aerodynamic performance of floating offshore wind turbines is essential for the further development of offshore wind farms. In this perspective, a developed Actuator line model is utilized to analyze an offshore turbine on four different platforms. The model reliability was examined through three sets of validations involving turbine output in fixed and floating conditions and wake expansion in terms of size and rate. The affected relative velocity by the platform motion contributes to the wake deformation and temporal effects on induced velocity. Angular platform motions produce a non-axisymmetric helical wake that raises the chance of meandering wake patterns. It was founded although platform movement generally can boost the recovery of mean velocity value, it may amplify the amplitude of velocity deficit fluctuation at further downstream by encouraging interactions and merging vortex rings. Consequently, the wake propagates into a form of stronger circles whose period, strength, and center are functions of turbine movement and operation conditions. By providing a computationally efficient tool, the findings emphasize the importance of wake propagation in designing and assessing farm layouts that operate in the presence of significant multi-motions of floating offshore wind turbines.