Sound absorption performance of a porous metal can be improved by compression and optimal permutation, which is favorable to promote its application in noise reduction. The 10-layer gradient compressed porous metal was proposed to obtain optimal sound absorption performance. A theoretical model of the sound absorption coefficient of the multilayer gradient compressed porous metal was constructed according to the Johnson-Champoux-Allard model. Optimal parameters for the best sound absorption performance of the 10-layer gradient compressed porous metal were achieved by a cuckoo search algorithm with the varied constraint conditions. Preliminary verification of the optimal sound absorber was conducted by the finite element simulation, and further experimental validation was obtained through the standing wave tube measurement. Consistencies among the theoretical data, the simulation data, and the experimental data proved accuracies of the theoretical sound absorption model, the cuckoo search optimization algorithm, and the finite element simulation method. For the investigated frequency ranges of 100–1000 Hz, 100–2000 Hz, 100–4000 Hz, and 100–6000 Hz, actual average sound absorption coefficients of optimal 10-layer gradient compressed porous metal were 0.3325, 0.5412, 0.7461, and 0.7617, respectively, which exhibited the larger sound absorption coefficients relative to those of the original porous metals and uniform 10-layer compressed porous metal with the same thickness of 20 mm.