A broadband absorber based on metamaterials of graphene and vanadium dioxide (VO2) is proposed and investigated in the terahertz (THz) regime, which can be used for switch applications with a dynamically variable bandwidth by electrically and thermally controlling the Fermi energy level of graphene and the conductivity of VO2, respectively. The proposed absorber turns ‘on’ from 1.5 to 5.4 THz, with the modulation depth reaching 97.1% and the absorptance exceeding 90% when the Fermi energy levels of graphene are set as 0.7 eV, and VO2 is in the metallic phase. On the contrary, the absorptance is close to zero and the absorber turns ‘off’ with the Fermi energy level setting at 0 eV and VO2 in the insulating phase. Furthermore, other four broadband absorption modes can be achieved utilizing the active materials graphene and VO2. The proposed terahertz absorber may benefit the areas of broadband switch, cloaking objects, THz communications and other applications.