We propose and demonstrate a modulatable all-silicon terahertz absorber based on a cylindrical metamaterial structure. Broadband absorption is obtained from 0.86 to 2.00 THz, with an average absorbance of 94%, indicating a wide absorption bandwidth of 1.14 THz. The maximum absorption, around 1.24 THz, is up to 98%. We employ simulation results to investigate the physical properties of the absorption, and we attribute the broadband absorption to a combination of electric dipole and magnetic dipole modes. Furthermore, the tunable response of the all-silicon terahertz absorber under the optical pump beam, with different fluences, is studied using a hierarchical model for simulating the carrier density of the gradient distribution. Moreover, different polarizations and oblique incidences of terahertz waves are used to verify the polarization and angle-of-incidence insensitivity of the device. The absorber provides a simple method to design a modulated broadband terahertz absorber, and the design scheme is scalable to develop various tunable broadband absorbers at other frequencies. This work holds great potential in modulator applications, imaging devices, and energy conversion.