This study addresses the effects of large-amplitude vibration on the pressure-dependent absorption of a structure multiple-cavity system. It is the first study to consider the effects of large-amplitude vibration and pressure-dependent absorption. Previous studies considered only one of these two factors in the absorption calculation of a perforated panel absorber. Nonlinear differential equations, which represent the structural vibration of a perforated panel absorber, are coupled with the wave equation, which represents the acoustic pressures induced within the cavities. The coupled nonlinear differential equations are solved with the proposed harmonic balance method, which has recently been adopted to solve nonlinear beam problems and other nonlinear structural-acoustic problems. Its main advantage is that when compared with the classical harmonic balance method, the proposed method generates fewer nonlinear algebraic equations during the solution process. In addition, the solution form of the nonlinear differential equations from this classical method can be expressed in terms of a set of symbolic parameters with various physical meanings. If a numerical method is used, there is no analytic solution form, and the final solution is a set of numerical values. The effects of the excitation magnitude, cavity depth, perforation ratio, and hole diameter on the sound absorption of a panel absorber are investigated, and mode and solution convergence studies are also performed. The solutions from the proposed harmonic balance method and a numerical integration method are compared. The numerical results show that the present harmonic balance solutions agree reasonably well with those obtained with the numerical integration method. Several important observations can be made. First, perforation nonlinearity is a very important factor in the absorption of a panel absorber at the off structural resonant frequency range. The settings of the hole diameter, perforation ratio, and cavity depth for optimal absorption differ greatly with consideration of perforation nonlinearity. Second, the “jump up phenomenon,” which does not occur in the case of linear perforation, is observed when perforation nonlinearity is considered. Third, one or more absorption troughs, which worsen the average absorption performance, may exist in cases with multiple cavities.