This work presents the design of a broadband frequencyselective surface absorber (FSSA) using laser-induced graphene (LIG). This type of resistive material composed of porous graphene has been analyzed, and its performance has been modeled through different cases of FSS based on LIG patches. The results of this analysis, both simulated and experimental, show the existence of periodic frequency bands of absorption ranging from a few GHz to 50 GHz. Taking advantage of this absorbing behavior, a single-layer FSSA, including a circular LIG patch at the center of the unit cell, is proposed. A circuit model for this FSSA unit cell is introduced, which allows us to efficiently improve the absorption over a large bandwidth by including an ad-hoc dielectric layer. The FSSA is fabricated and measured: the experimental results show a good agreement with the simulated ones, providing absorption of more than 0.9 from 14 GHz to 48 GHz (109.7% relative bandwidth). In addition, the proposed design exhibits robust behavior to both TE and TM oblique incidence up to 45º.