We present a broadband and tunable graphene-based absorber in the terahertz (THz) region, which is composed of a monolayer of graphene square-shaped patch with fourfold rotationally symmetric groove and a metallic ground film separated by a silicon dioxide (SiO2) spacer layer. The bandwidth of 90% absorbance for the structure reaches up to 1.66 THz with a central frequency of 2.53 THz under normal incidence, and the broadband absorption still remains 80% over a wide incident angles up to 50° for both transverse electric (TE) and transverse magnetic (TM) modes. Furthermore, the peak absorption of the proposed absorber can be tuned from 15% to near 100% by varying the graphene's Fermi energy from 0 to 1.0 eV via adjusting the bias voltage of the graphene layer or chemical doping. Due to the geometrical symmetry, the proposed structure is insensitive to the polarization state of incidence wave. Benefits from these outstanding performances, we believe that our proposed absorber may have great applications in tunable THz filtering, imaging, and cloaking.