In this paper, a dynamic tunable graphene and metamaterial absorber with a periodic structure, composed of graphene and cross groove medium, is proposed. The results show that the absorption efficiency of the absorber is close to 100%, and by changing the chemical potential from 0.4 eV to 0.8 eV, the absorption peak can be adjusted from 6.4 THz to 8.75 THz, from 13.1 THz to 17.85 THz. The simulated electric field and power loss density distribution reveal that the absorption mainly comes from the excitation of continuous surface plasmon resonance on graphene structure. In addition, the absorber is insensitive to polarization, because both transverse electric and transverse magnetic modes have the geometric rotational symmetry of the unit structure. Furthermore, the absorption characteristics of the absorber can be adjusted dynamically by changing the chemical potential of graphene. The simulated results shows that the absorptivity is sensitive to the incident angle of the THz wave, which means this material can be used as angle sensors in the future.