Stealth technology is of great importance and significance in reducing the radar cross section and improving the survivability of the target aircraft. Absorber is one of the most important structures in stealth technology. However, the present investigations of absorbers mainly focus on the narrow band or multi-band. To extend the operation bandwidth, a graphene-based absorber structure is proposed in this paper. The proposed absorber has a periodic structure whose unit cell consists of a square and a circular graphene-based ring. The surface impedance of the periodic structure can be optimized to match the impedance of the free space in a very wide band by adjusting the electrostatic bias voltage. Then the operation band is significantly extended. By using the commercial software, CST Microwave Studio 2014, the performance of the proposed absorber is studied. The simulated results show that the proposed absorber can absorb electromagnetic (EM) waves in an ultra-wideband from 2.1 to 9.0 GHz, with an absorbing rate of up to 90%. Moreover, the proposed absorber is insensitive to the polarization of the incident wave due to the symmetry of the structure. We also find that the absorber can be tuned to work at any frequency in a range from 2.0 to 9.0 GHz for a fixed geometrical parameter. The equivalent circuit model (ECM) approach and interference theory (INF) are employed to investigate the physical mechanism of the proposed absorber. According to the ECM, we analyze the resonant characteristics of the square and circular graphene rings. Owing to the existence of two different graphene rings, two resonant frequencies are detected. By optimizing the structure parameters of the graphene rings, the two resonant frequencies are brought closer, resulting in the increase of the operation band. On the other hand, the real part of the input impedance of the equivalent circuit reaches up to about 300 Ω and the imaginary part is close to 0 Ω, which provides good matching to the free space, leading to high absorption rate. According to the interference theory, the amplitudes and phases of the direct reflection and the multiple reflections of EM waves are studied. It is found that the destructive interference between the direct reflection and multiple reflection makes the absorber have high performance in an ultra-wideband. The results obtained from ECM and INF are in good agreement with the simulation ones.