We proposed an effective design of multifunctional switchable broadband terahertz absorber based on hybrid graphene-vanadium dioxide metamaterials. Due to the symmetry of the unit cell, the absorber has polarization-insensitive properties when electromagnetic waves are incident perpendicularly, and can still maintain excellent absorption performance over a wide range of incident angles. Numerical simulation results show that the amplitude of the broadband absorption (from 1.69 THz to 3.21 THz) can be dynamically adjusted by adjusting the conductivity of the vanadium dioxide due to its unique transition characteristics from insulator to metal. Furthermore, by applying an external bias voltage to adjust the Fermi energy of graphene, the peak absorptance of the proposed absorber in the same broadband can be dynamically tuned from 0.226 to 0.992. By altering the two independently controllable parameters (the conductivity of vanadium dioxide and graphene''s Fermi energy) simultaneously, the proposed device can be switched among a transparent insulating dielectric, a perfect reflector, and a broadband absorber in a wide frequency range. The designed system can be extended to the infrared and visible bands, offering a new method for high-performance terahertz devices.