To improve the sound absorption performance of traditional acoustic coatings under static pressure and in low-frequency ranges, a novel acoustic coating was designed by embedding multi-scale acoustic black holes (ABHs) within a compliant matrix. A theoretical model of the coating was established using the equivalent medium method and transfer matrix method, and its acoustic computational model was constructed in COMSOL for comparative validation. Simulations were conducted to analyze the maximum deformation and sound absorption performance of the coating under different static pressures, investigating its deformation and sound absorption mechanisms while assessing the influence of key parameters on pressure resistance and acoustic performance. Ultimately, optimization of the material and geometric parameters yielded an acoustic coating unit exhibiting superior pressure resistance and sound absorption performance.