We design an actively tunable polarization-sensitive multiband absorber in the mid-infrared region,which consists of stacked graphene multilayers separated by dielectric layers on a metal mirror.Benefiting from the anisotropic structure,the absorber has dual absorption bands with almost perfect absorption at different wavelengths under the x and y polarizations.Analyzing the electric field amplitude distributions and the surface currents,we find that the absorption peaks under the same polarization are excited in the graphene layers independently.Therefore,more absorption bands can be achieved by increasing the graphene layers.Adjusting the Fermi energy of the graphene layers,the working wavelengths of the polarization-sensitive multiband absorbers can be tuned actively,and thus achieving a wide band regulation range.Besides,the peak number and the peak strength of the multiband absorber can be actively controlled by the polarization angle as well.We also propose a method to design an actively tunable polarization-sensitive multiband absorber,which may have potential applications in mid-infrared devices,such as polarization-sensitive filters and detectors.