In order to expand the relative absorption bandwidth of terahertz absorber, an ultra-thin, wide-band, and tunable terahertz absorber based on graphene metamaterial is designed, which is composed of patterned graphene layer, dielectric layer, and metal reflection substrate. The simulation results show that the absorptivity of the absorber at 4.48 THz frequency is 99.98%, and the absorptivity at this frequency can be changed to 25.08% by adjusting the chemical potential of graphene. At the same time, the absorber shows the absorption characteristic of insensitive to the polarization of incident wave, and can still maintain a certain wide-band absorption characteristic when the terahertz wave is tilted. On this basis, a terahertz absorber based on three-layer patterned graphene is designed, which can further expand the absorption bandwidth. The simulation results show that the absorption rate of the absorber is higher than 90%, and the relative absorption bandwidth is 97% between 1.90 THz and 5.49 THz.