Terahertz metamaterial absorbers, as a kind of important terahertz functional devices, are widely used in biomedical sensing, electromagnetic stealth, military radar and other fields. However, this traditional metamaterial absorber structure has disadvantages such as poor tenability, single function and insufficient performance indexes, which can no longer meet the complex and changeable electromagnetic environment requirements. Therefore, the tunable metamaterial absorber has gradually become a research hotspot in the field of terahertz functional devices. In order to achieve the tuning of the absorption characteristics of the metamaterial absorber, the electromagnetic characteristics of the resonance unit or the substrate material or the geometric size of the metamaterial structural unit are usually adjusted. A terahertz broadband tunable metamaterial absorber based on graphene and vanadium dioxide is proposed in this paper. The absorber consists of a vanadium dioxide resonant layer, a continuous graphene layer and a metal reflector separated by a Topa’s medium. The numerical simulation results show that when the material is in the all-metal state (electrical conductivity of 200 000 S·m^-1), and the Fermi energy of graphene is set as 0.1 eV, the absorption bandwidth of more than 90% reaches 2.8 THz. When the Fermi energy of graphene is adjusted to change between 0.1 and 0.3 eV, the operating frequency of the absorber shows an obvious blue shift. The proposed broadband structure can switch freely between the reflector and the absorber when the conductivity of vanadium dioxide varies between 100200 000 S·m^-1 due to the phase transformation characteristics of vanadium dioxide material from the insulating state to the metallic state. In addition, the surface current distribution of the metamaterial absorber at the three perfect absorption peaks of 1.87, 3.04 and 4.16 THz was monitored respectively, and its working mechanism was discussed. The structure designed in this paper realizes the dual control of the absorber’s operating frequency and absorption amplitude through two independent adjustable “switches” of graphene and vanadium dioxide, which provides a new development idea for the design of multifunctional terahertz devices.