In this paper, the instability of a two-dimensional plate with initial curvature in low speed axial flow is studied. The aerodynamic forces acting on the curved plate is obtained based on the thin airfoil theory, which is also verfied by a wind tunnel test. The nonlinear motion equation is transferred into ordinary differential equations by the Galerkin′s method,the Newton iteration method is applied for the static deformation. The bifurcation structure is analyzed in the parametric planes and spaces. The results show that the theoretical calculations of the pressure show a good agreement with the wind test; after the dynamical pressure exceeds the critical values, the system undergoes a non-symmetric static bifurcation with the appearances of new stable and unstable equilibrium points; the critical dynamic pressure increases (decreases) with the increasing of the in-plane tension (pressure); however, as the initial curvature increasing the critical dynamic first increases and then decreases; there are four types of bifurcations in different regions of the parametric plane; the responses of the system is close bound up with the dynamic pressure and the initial conditions.