This study presents a tri-layer broadband metamaterial absorber that operates in the GHz range. The absorber was composed of a polyhedral iron-cobalt alloy/graphite nanosheet material arranged in a flat sheet with two punched-in rings for the top layer, a continuous FR-4 layer at the middle, and a continuous copper layer at the bottom. For the normal incidence of the electromagnetic wave, the proposed absorber demonstrated an exceptional broadband absorption in a frequency range of 7.9–14.6 GHz, revealing an absorption exceeding 90%. The absorption magnitude remains to be above 90% in a frequency range of 8–11.1 GHz for transverse-electric-polarized waves at incident angles up to 55°. For both the transverse-magnetic- and electric-polarized waves, the absorption exceeds 90% in a frequency range of 9.5–14.6 GHz. The physical mechanism behind the absorption properties is analyzed thoroughly through the electric and magnetic field distributions. The obtained results could contribute potentially to the development of microwave applications based on metamaterial absorbers, such as radar-stealth technology, electromagnetic shielding for health safety, and reduced electromagnetic interferences for high-performance communications and electronic devices.