The flutter of two dimensional sandwich panel with supersonic aerodynamic loading on one side is studied. The flutter critical Mach number and the effect of viscous damping are studied by using the Galerkin method and the complex modal method. The results show that the flutter occurs when the first and the second mode natural frequency coalesce, where the vibration energy accumulation starts to be positive. Considering the viscoelasticity of the mid layer, the results show that with the increase of viscous damping, the critical flutter Mach number and the corresponding critical flutter frequency of the system will decrease at first and then increase. It is concluded that the reason for this phenomenon is due to the dual effect of the viscous damping. The viscous damping can reduce the natural frequency to make the system less stable at one hand, and absorb energy which enhances the stability at the other hand. The system appears complex phenomenon as the result of dual effects of the viscous damping. The conclusions of this research will be meaningful in the design of composite panels in supersonic flow.