A 2-dimensional rigid airfoil with a control surface is simplified to 3-DOF aeroelastic model. This 3-DOF aeroelastic model took a cubic nonlinear stiffness in heaving and pitching displacement directions, and employed bilinear stiffness for the clearance in the control surface. Based on the principle of target energy transfer, a single degree of nonlinear energy sinker is coupled with the airfoil structure for suppressing the flutter of the system. Considering the quasi steady aerodynamic theory, the motion equations of the two systems (with and without NES) are established. Meanwhile, the peak-peak amplitude diagrams show that the global dynamic property of the system is changed by attaching a NES. Bifurcation diagrams is also constructed by using numerical continuation method for both systems. The Comparison of the bifurcation diagrams exhibits the suppressing effect of the NES, and it is find that aeroelastic instability was partially or even completely suppressed by passively transferring vibration energy from the wing to the NES in a one-way irreversible fashion.