This paper studies the flutter of a two-dimensional airfoil in the supersonic flow with cubic physical and aerodynamic non-linearity. First, the characteristic value of the system in the neighborhood of equilibrium point is analyzed. The parametric equations of flutter are obtained in the vicinity of Hopf bifurcation point. Then, the normal form of Hopf bifurcation is deduced by applying the normal form direct method. The dependence of response on initial values is certified by numerical analysis in the super- and sub-critical cases. Finally, study on the topological structure of bifurcation shows that the “hard” structural non-linearities render the airfoil safer, whereas the “soft” ones render the airfoil unsafe. In other respect, increasing the distance between the center of mass and the elastic axis appears to be beneficial from the point of view of the aeroelastic response.