A novel acoustic metamaterial is proposed by making micro-perforations on both the top facesheet and the corrugate plates of sandwich plate with honeycomb-corrugation hybrid core. The hybrid-cored metamaterial is ultra-lightweight, occupies a small volume, and exhibits excellent mechanical properties and good low-frequency sound absorption property. Based on the classical Maa theory of thin plates with micro-perforations, a theoretical model of sound absorption is established for the proposed metamaterial. The method of finite elements is subsequently used to validate the model, showing that their good agreement is achieved. Physical mechanism behind the energy dissipation in each sub-structure of the metamaterial is explored. It is found that the main route of energy dissipation is via viscous effect at the micro-perforation, and thermal dissipation is negligible. The influence of key geometrical parameters, such as upper facesheet thickness, perforation diameter and corrugated plate thickness, on sound absorption is systematically investigated. The present results are helpful for designing multifunctional lightweight materials/structures for simultaneous load-bearing, energy absorption and noise control.