In this study, flutter of blades in floating horizontal-axis wind turbines is investigated. The blade is modeled as a non-uniform Euler-Bernoulli beam in bending and torsion, which can experience large deflections. The discretized form of the aeroelastic governing equations of the blade is obtained by combining blade element momentum theory (BEM) and geometrically exact beam theory (GEBT). To emulate the true physical and geometrical properties of the blade, for each property, a mathematical function that has been fit to the series of data points corresponding to the NREL 5 MW turbine blade is constructed and used in the aeroelastic governing equations. Numerical results are compared with the results obtained from the ABAQUS software and good agreement is observed. Results are presented for both parked and operational wind turbine rotors. Results show the significant effect of the turbine tower rotation, due to wave action, on the aeroelastic stability of the blades. Furthermore, it is shown that coupled motion of the platform as a rigid body with rotor angular velocity can lead to flutter instability at low wind speeds.