Metal-insulator-metal-based plasmonic metamaterial absorbers (MIM-PMAs) generate strong localized surface plasmon resonance (LSPR) on their surfaces. Therefore, MIM-PMAs are expected to enhance the absorption of graphene coated on their surfaces. Graphene-coated MIM-PMAs (GMIM-PMAs) were developed and their optical properties were investigated both experimentally and numerically at infrared wavelengths. Significant modification of the absorption of GMIM-PMAs was achieved only in the main LSPR wavelength region, where the insulator is lossless. The enhancement of the absorption of graphene could be maximized by the optimization of the insulator thickness of the MIM-PMAs. The results obtained here are expected to contribute to the development of high-responsivity graphene-based photodetectors and optoelectronic devices.