An acoustic absorption structure of a double-layer porous metal material with air layers is proposed. The Johnson-Champoux-Allard (JCA) model combined with the transfer matrix method (TMM) was used to establish the theoretical calculation model of the sound absorption coefficient (SAC). Meanwhile, the SAC between 500 and 6300 Hz were measured with an impedance tube. The errors between the theoretical and experimental values were compared to illustrate the good predictability of the theoretical model within the inverse estimations of the transport properties. The effects of the material placement order, material thickness, and cavity depth on the sound absorption performance from 200 to 5000 Hz were analyzed using the theoretical model. Further, a multi-objective function genetic algorithm was used to optimize the porous material's thickness and SAC to obtain an acoustic structure with a smaller thickness and higher sound absorption. A series of optimal solutions were obtained for acoustic structures with a total thickness of less than 70 mm. When the total thickness of the foam metal was 33.57 mm, the average SAC reached 0.853, which was significantly lower than the total thickness of the previous experiments. The multi-objective function genetic algorithm can provide a reliable solution for the optimal design of most sound-absorbing structures.