The effect of structural paramters on the response and aerodynamic stiffness characteristics of the free aeroelastic system under the influence of dynamic stall is investigated adopting CFD (Computational Fluid Dynamics) method. The equilibrium angle of the spring and the structural stiffness are taken as parameters of interest. Systems with small equilibrium angles enter the symmetric limit-cycle state more quickly after a Hopf bifurcation and experience dynamic stall in both directions, rather than slowly decreasing in minimum angle of attack and remaining in the asymmetric limit-cycle state before dynamic stall in the opposite direction, as is the case with systems with large spring equilibrium angles. Thus, aerodynamic stiffness of system with large equilibrium angles can be more significantly influenced by the change in aerodynamic moment characteristics at the minimum angle of attack. Furthermore, by increasing the initial angular velocity, we find that the system response all becomes symmetric limit cycle and therefore the aerodynamic stiffness appears to have a monotonically increasing characteristic. As to the effect of structural stiffness, it is found that the limit cycle amplitude first increases with structural stiffness after bifurcation, then the amplitude is unchanged with varying structural stiffness at higher Mach number. Energy maps show that the parametric distribution of the energy transfer contributes to this phenomenon. Moreover, when entering the symmetric limit cycle state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the increase in the aerodynamic stiffness is determined solely by the increase in dynamic pressure without the effect of changes in moment characteristics.