We design and propose a five-band absorber based on graphene metamaterial for the terahertz (THz) sensing field. The localized surface plasmon resonances of patterned graphene are excited, contributing to five tunable ultra-narrow absorption peaks, which are specified by the electric field distributions. Moreover, the absorber is insensitive to different polarization modes and incident angles. When increasing the Fermi level of the patterned graphene, which is composed of a round ring and a square ring connected by four thin wires, the resonant frequencies exhibit distinct blue shifts. For refractive index sensing, due to the addition of a continuous dielectric groove, the theoretical results show that the maximum averaged normalized sensitivity, Q factor, and FOM can reach 0.647 RIU−1 (refractive index unit, RIU), 355.94, and 215.25 RIU−1, indicating that the sensing performances are further enhanced compared with previous works. As a result, the proposed structure may provide a new method to realize ultrasensing in the THz region.