A bifunctional absorber with hybrid graphene–vanadium dioxide (VO2) is proposed and numerically investigated in the paper. Simulation results indicate that the absorber behaves as a broadband absorber with absorptance of more than 90% from 3.15 THz to 8.45 THz, when VO2 is in the metallic state. When VO2 is in the insulating state, the design exhibits a 10-band absorber, whose peak absorptances are above 90%. Broadband absorption is investigated by the impedance matching theory, and detailed physical studies indicate that it arises from electromagnetic resonance based on VO2 patches. Ten-band absorption originates from graphene plasmon (GP) resonance and Fabry–Perot cavity resonance. By adjusting the conductivity of VO2 and the Fermi level of graphene, the designed absorber not only can be independently tuned, but also has 91.9% modulation depth under broadband absorptance. Furthermore, the effect of incident angle on absorptance is investigated, and the absorber is polarization insensitive due to the symmetry of the structure. Benefiting from the above excellent performance, the bifunctional absorber offers great potential in terahertz applications, such as modulating, switching, and electromagnetic energy harvesting.