The composite structure of a microperforated panel and porous metal is a promising sound absorber for industrial noise reduction, sound absorption performance of which can be improved through parameter optimization. A theoretical model is constructed for the composite structure of a microperforated panel and porous metal based on Maa’s theory and the Johnson–Champoux–Allard model. When the limited total thickness is 30 mm, 50 mm, and 100 mm respectively, dimensional optimization of structural parameters of the proposed composite structure is conducted for the optimal average sound absorption coefficient in the frequency range (2000 Hz, 6000 Hz) through a cuckoo search algorithm. Simulation models of the composite structures with optimal structural parameters are constructed based on the finite element method. Validations of the optimal composite structures are conducted based on the standing wave tube method. Comparative analysis of the theoretical data, simulation data, and experimental data validates feasibility and effectiveness of the parameter optimization. The optimal sandwich structure with an actual total thickness of 36.8 mm can obtain the average sound absorption coefficient of 97.65% in the frequency range (2000 Hz, 6000 Hz), which is favorable to promote practical application of the composite structures in the fields of sound absorption and noise reduction.