A kind of functional graphene thin film metamaterial on a metal-plane separated by a thick dielectric layer is designed for terahertz (THz) absorbers. We investigate the properties of the graphene metamaterial with different interlayers in the 0–3 THz range. The simulation results show that the absorption rate reaches up to 99.9% at the frequency of 1.917 THz. Changing the period to 80 μm×18 μm can get a narrow-band high quality factor (Q) absorber. We present a novel theoretical interpretation based on the standing wave field theory, which shows that the coherent superposition of incident and reflection rays produces standing waves, and the field energy is localized inside the thick spacers and dissipates through the metal-planes.