Acoustic metamaterial structures have received extensive attention for sound and vibration engineering applications from the scientific community in recent years. However, the real-life application of conventional acoustic metamaterial structures is frequently limited by fixed frequency bands and increased structural thicknesses in low-frequency noise reduction. In this study, we introduce an origami-based acoustic metamaterial structure that consists of a Miura-ori foldcore, along with a perforated and an unperforated panel. The proposed Miura-ori foldcore sandwich acoustic metastructure (MOF-SAM) exhibits adjustable low-frequency sound absorption capacities due to the foldability of the origami foldcore. Moreover, we employ numerical methods to investigate the sound absorption properties of the MOF-SAM, quantified by the sound absorption coefficient. The results indicate that the structure has a single absorption peak which is superior to that of acoustic structures composed of conventional honeycomb cores. The dissipation of acoustic energy is due to the structural vibrations of the metastructure and the losses in the folding process of the origami foldcore. The numerical results of this study show that the proposed sound absorption mechanism enables tunable low-frequency sound absorption. The geometric design and periodicity of the origami unit fragments offer multiple distinct absorption peaks and thus tunable acoustic performance. These findings of this study are expected to inspire novel designs for next-generation acoustic devices.