The accurate prediction of unsteady aerodynamic performance and loads, for floating offshore wind turbines (FOWTs), is still questionable because several conventional methods widely used for this purpose are applied in ways that violate the theoretical assumptions of their original formulation. The major objective of the present study is to investigate the unsteady aerodynamic effects for the rotating blade due to the periodic surge motions of an FOWT. This work was conducted using several numerical approaches, particularly unsteady computational fluid dynamics (CFD) with an overset grid-based approach. The unsteady aerodynamic effects that occur when an FOWT is subjected to the surge motion of its floating support platform is assumed as a sinusoidal function. The present CFD simulation based on an overset grid approach provides a sophisticated numerical model on complex flows around the rotating blades simultaneously having the platform surge motion. In addition, an in-house unsteady blade element momentum (UBEM) and the fast (fatigue, aerodynamic, structure, and turbulence) codes are also applied as conventional approaches. The unsteady aerodynamic performances and loads of the rotating blade are shown to be changed considerably depending on the amplitude and frequency of the platform surge motion. The results for the flow interaction phenomena between the oscillating motions of the rotating wind turbine blades and the generated blade-tip vortices are presented and investigated in detail.