A composite structure composed of a porous-material layer mosaicked with a perforated resonator is proposed to improve the low-frequency sound absorption of the porous layer. This structure is investigated in the form of a porous-material matrix (PM) and a perforated resonator (PR), and the PR is a thin perforated plate filled with porous material in its back cavity. Theoretical and numerical models are established to predict the acoustic impedance and sound absorption coefficient of the proposed structure, and two samples made of polyurethane and melamine, respectively, are tested in an impedance tube. The predicted results are consistent with that of the measured. Compared with a single porous layer with the same thickness, the results show that the designed structure provides an additional sound absorption peak at low frequencies. The proposed structure is compact and has an effective absorption bandwidth of more than two octaves especially below the frequency corresponding to 1/4 wavelength. A comparison is also made between the sound absorption coefficients of the proposed structure and a classical micro-perforated plate (MPP), and the results reveal equivalent acoustic performance, suggesting that it can be used as an alternative to the MPP for low–mid frequency sound absorption. Moreover, the influences of the main parameters on the sound absorption coefficient of PPCS are also analyzed, such as the hole diameter, area ratio, flow resistance, and porous-material thickness in the PR. The mechanism of sound absorption is discussed through the surface acoustic impedance and the distributions of particle velocity and sound pressure at several specific frequencies. This work provides a new idea for the applications of the thin porous layer in low- and medium-frequency sound absorption.