The aerodynamic flutter and flutter suppression of graphene-reinforced composite plates with cantilever boundary conditions are studied. The equivalent material parameters of graphene-reinforced composites are calculated using Halpin-Tsai and the law of mixing ratio. According to the classical plate theory， the second type of piezoelectric equations and Hamilton''s principle， the motion equations of the structure are obtained. The natural frequency of the graphene composite cantilever plate is calculated by the Rayleigh-Ritz method. The influences of the three different distribution types （X-GPLs， U-GPLs and O-GPLs distribution） and the mass fraction of different graphene reinforcements on the structural natural frequency and the dimensionless flutter aerodynamic pressure are explored. The control effects of acceleration feedback and displacement feedback on aerodynamic flutter of the structure are studied. The numerical simulation demonstrates that， as the mass fraction of graphene increases， the natural frequency and dimensionless flutter aerodynamic pressure of the graphene-reinforced composite plate increase. The X-GPLs distribution has the better aerodynamic performance than the U-GPLs distribution and O-GPLs distribution. Both acceleration feedback and displacement feedback controls can effectively suppress the aerodynamic flutter of the structure and improve the aerodynamic stability of the structure.