A novel metamaterial absorber based on a graphene-metal hybrid structure is proposed. The amplitude tunability at single frequency and broadband frequency within the microwave domain is realized via the change of graphene Fermi level by altering the applied voltage. The mechanisms of absorption and amplitude tunability of electromagnetic field are illustrated. The numerical simulation of this metamaterial structure under single frequency band is made. The results show that, when the structural parameters are fixed, the absorption intensity of absorber decreases with the increase of graphene Femi level and the maximum modulation depth reaches 58.6%. When the graphene Fermi level is 0 eV, the center frequency changes with the structural parameters. An array composed of unit structures with different sizes is used to realize the characteristic of the broadband wave absorption based on the multi-absorption-peak superimposed expansion bandwidth principle. The property of amplitude tunability possessed by this broadband absorber is confirmed by numerical simulations.