We proposed a dual-controlled broadband terahertz (THz) absorber based on graphene and Dirac semimetal. Calculated results show that the absorptance over 90% is achieved in the frequency range of 4.79-8.99 THz for both transverse electric (TE) and transverse magnetic (TM) polarizations. Benefiting from the advantage of the dielectric constant of these materials varying with chemical doping or gate voltage, the simulation results exhibit that the absorbance bandwidth can be controlled independently or jointly by varying the Fermi energy of the graphene or Dirac semimetal patterns instead of redesigning the absorbers. Impedance matching theory was introduced to analyze the absorption spectra changing with EF. The bandwidth and absorptivity of the proposed absorber are almost independent of changing the incident angle θ up to 35° and 40° for TE and TM modes, respectively. It works well even at a larger incident angle. Because of the symmetry of the structure, this designed absorber is polarization insensitive and almost the same absorptivity for both polarizations. Furthermore, the physical mechanisms were further disclosed by the electric field distributions. The proposed broadband and dual-controlled absorber may have potential applications in various fields of high-performance terahertz devices.