Numerical simulations of the flow around a periodically vibrating airfoil and the two-degree-of-freedom (TDOF) bending-torsion flutter characteristics were carried out. An unsteady, two-dimensional, incompressible Navier-Stokes flow solver was coupled with a two-degree-of-freedom structural model for a flutter computation. To simulate unsteady phenomena, the Navier-Stokes equations are described by the ALE method. The Baldwin-Lomax turbulence model was implemented for high Reynolds number calculations. Computations of the periodically vibrating airfoil show agreement with Theodorsen's linearized theory and the existing results of some numerical analyses. Flutter was observed in the TDOF model coupled with the flow solver when the rigidity of the airfoil was small. A control method for the flow field was studied and the airfoil flutter was stabilized by a PID (Proportional-Integral-Derivative) control algorithm.