A dual-controlled tunable broadband terahertz absorber based on a hybrid graphene-Dirac semimetal structure is designed and studied. Owing to the flexible tunability of the surface conductivity of graphene and relative permittivity of Dirac semimetal, the absorption bandwidth can be tuned independently or jointly by shifting the Fermi energy through chemical doping or applying gate voltage. Under normal incidence, the device exhibits a high absorption larger than 90% over a broad range of 4.06–10.7 THz for both TE and TM polarizations. Moreover, the absorber is insensitive to incident angles, yielding a high absorption over 90% at a large incident angle of 60° and 70° for TE and TM modes, respectively. The structure shows great potential in miniaturized ultra-broadband terahertz absorbers and related applications.