In order to accurately study the effect of curvature on panel aeroelastic behaviors, a fluid-structure coupling algorithm is adopted to analyze the curved panel flutter in transonic and supersonic airflows. First, the governing equation for the motion of the curved panel and the structure solver are presented. Then the fluid governing equations, the fluid solver and the fluid-structure coupling algorithm are introduced briefly. Finally, rich aeroelastic responses of the curved panel are captured using this algorithm. And the mechanisms of them are explored by various analysis tools. It is found that the curvature produces initial aerodynamic load above the panel. Thus the static aeroelastic deformation exists for the curved panel in stable state. At Mach 2, with its stability lost on this static aeroelastic deformation, the curved panel shows asymmetric flutter. At Mach 0.8 and 0.9, the curved panel exhibits only positive static aeroelastic deformation due to this initial aerodynamic load. At Mach 1.0, as the dynamic pressure increases, the curved panel loses its static and dynamic stability in succession, and behaves static aeroelastic deformation, divergence and flutter consequentially. At Mach 1.2, with its stability lost, the curved panel flutters more violently towards the negative direction. The results obtained could guide the panel design and panel flutter suppression for flight vehicles with high performances.