In the present study, a numerical framework for predicting the aerodynamic performance and the aeroelastic behavior of floating offshore wind turbine rotor blades involving platform motion was developed. For this purpose, the aerodynamic and structural analyses were conducted simultaneously in a tightly coupled manner by exchanging the information about the aerodynamic loads and the elastic blade deformations at every time step. The elastic behavior of the turbine rotor blades was described by adopting a structural model based on the Euler-Bernoulli beam. The aerodynamic loads by the rotor blades were evaluated by adopting a blade element momentum theory. The numerical simulations were conducted when the platform of the wind turbine independently moves in each of the six degrees-of-freedom directions consisting of heave, sway, surge, roll, pitch, and yaw. It was observed that flexible blades exhibit complicated vibratory behaviors when they are excited by the aerodynamic, inertia, and gravitational forces simultaneously. It was found that the load variation caused by the platform surge or pitch motion has a significant influence on the flapwise and torsional deformations of the rotor blades. The torsional deformation mainly occurs in the nose-down direction, and results in a reduction of the aerodynamic loads. It was also found that the flapwise root bending moment is mainly influenced by the platform surge and pitch motions. On the other hand, the edgewise bending moment is mostly dictated by the gravitational force, but is not affected much by the platform motion.