Terahertz absorbers play a crucial role in terahertz detectors, radar stealth, electromagnetic shielding, and other fields. However, the design and fabrication of flexible terahertz broadband absorbers remain a challenge at present. Here, we demonstrated a terahertz broadband absorber based on a copper composite film (CCF) consisting of a copper foam and an organic silica gel doped with Fe3O4 powder. The CCF can be fabricated by the infiltration method. The influence of the thickness and the pore size of the copper foam and the mass fraction of doped Fe3O4 powder on the absorption bandwidth were investigated. When the thickness of the CCF is 1.5 mm, the pore size of the copper foam is 95 pores per inch (ppi), and the mass fraction of Fe3O4 is 1%; a broadband absorption is achieved in the range of 0.11-3.5 THz. It is noted that the mass fraction of Fe3O4 has a significant impact on the absorption bandwidth. In addition, the thickness of the CCF and the pore size of the copper foam also have an impact on the absorption. The impedance matching theory is introduced to understand the mechanism of broadband absorption. This flexible broadband absorber has potential application in terahertz stealth, shielding, and the sixth-generation (6G) broadband wireless communication in the future.