We have investigated the effects of substrate phonon absorption on the resonance behavior of metal–insulator–metal (MIM) double-layer metamaterial absorbers (MMAs) in the terahertz (THz) frequency range. A sharp resonant absorption dip is clearly observed for a metamaterial-on-ground-plane (MMOGP) structure fabricated on a semi-insulating (SI) GaAs substrate when THz radiation is incident from the surface metamaterials (MMs) side. However, when the THz is incident from the substrate side to the ground-plane-on-metamaterial (GPOMM) structures fabricated on a SI GaAs substrate, we find that the resonance dip is almost merged into the broad background of acoustic phonon absorption. The resonant absorption is recovered when the GaAs substrate is replaced with a high-resistivity Si substrate. These findings demonstrate that the choice of substrates is very important to suppress the absorption by acoustic phonons absorption in the THz range and achieve high-quality factor resonance.