A Fractal metasurface-based absorber is designed to obtain a wideband absorption in THz frequency band. The developed absorber has a broadband absorption over more than 600 GHz bandwidth, from 0.6 THz to 1.2 THz, with a minimum absorption percentage of 70% and total absorption from 1 to 1.1 THz. The proposed fractal structure is investigated using a Modified Split Ring Resonator (MSRR). The absorption coefficient of the proposed fractal metasurface is compared with the modified initially SRR metasurface. The results indicate that by using fractal design, the metasurface operating band is summed up, resulting in a wide bandwidth. The absorption coefficient of the proposed fractal metasurface is studied using two different simulation software programs to ensure the obtained results, with a high agreement between the results of them. The designed metasurface has a similar absorption response for the different polarization of the incident wave. The impedance of the designed metasurface indicates that, for the operating band, the fractal metasurface has a surface impedance of around 377 Ω, indicating a good matching between the designed metasurface and air. Different incidence and polarization angles are studied with results showing its insensitivity to both of them. The designed metasurface is compared with previously published works, showing wider bandwidth, higher absorption, and incidence and polarization insensitivity. The proposed metasurface absorber can be used for biomedical applications.