Effects of microstructure factors on the acoustic performance of open-cell foams can be characterized numerically by a microstructure-based approach. To this regard, the numerical homogenization approach and the equivalent-fluid theory are employed to study the acoustic behavior of random open-cell foams within their Voronoi tessellation-based Representative Volume Elements (RVE). As a validation step, the numerical predictions are compared with the reference findings to either verify the finite element procedure or demonstrate that the constructed RVE can capture both the local geometrical characteristics and the acoustic macrobehavior of cellular solid foams. It can be seen from the obtained results that the morphological characteristics of open-cell foams could be controlled to achieve the desired sound absorbing behavior. In addition, the analytical expressions, formulating the relationship between the geometry of foam absorbers and their target absorption performance, are established to design sound absorbing foam layers.