A broadband tunable metamaterial graphene absorber is investigated in this paper. The unit cell of the proposed metamaterial graphene absorber is composed of four patch resonators. By tuning the chemical potential of graphene and the geometric size of each patch, the simulated total reflectivity is less than -10 dB from 22.02 to 36.61 THz and with the total thickness of 0.76 um (only 0.09λ at the lowest frequency). The analysis of the surface current, magnetic field and power flow distributions has been performed to better understand the absorption mechanism. Moreover, this proposed absorber achieves its bandwidth tunable characteristics through a voltage biasing of the graphene's Fremi level. This proposed metamaterial graphene absorber (MGA) could be used as smart absorbers, photovoltaic devices and tunable sensors.