In this paper, a five-band metamaterial absorber with a tunable function in a terahertz band is proposed, which consists of a gold grounding layer, a polyimide dielectric layer, and a periodic patterned graphene layer. The patterned graphene layer is constructed from two sets of copper-coin-shaped structures of different sizes. The designed absorber achieves absorptions of 96.4%, 99.4%, 99.8%, 98.4%, and 99.9% at 4.62 THz, 7.29 THz, 7.70 THz, 8.19 THz, and 8.93 THz, respectively, with an average absorption intensity of 98.78%. The physical mechanism of this five-band absorber was explained by the impedance matching principle and electric field distribution. The absorption performance of the five-band absorber can be effectively tuned by changing the geometry of the patterned graphene array and the thickness of the dielectric layer. Given that the resonant frequency of the absorber varies in proportion to the Fermi level, by varying the Fermi level of the graphene hypersurface, we can achieve the continuous tuning of the absorption performance over a wide frequency range. The five-band absorber has a stable absorption performance over a wide incidence angle of 0–65°, and by combining the merits of high absorption, dynamic adjustability, and a large number of absorption peaks, the given absorber could have great potential for applications in nondestructive testing, imaging, communication, sensing, and detectors.