This paper describes a new design method for optimizing the thickness distribution of a multilayered structure located on the coupling surface between a structure and an acoustic cavity. The design method incorporates a transfer matrix for the multilayered structure including a poroelastic media layer. The one-dimensional transfer matrix adopted here is an approximate representation addressing vibro-acoustic effects inherent in a multilayered structure and balances calculation times and desired accuracy. In this study, the problem of minimizing the acoustic pressure is formulated under the volume constraint. Numerical results show that acoustic response is significantly reduced by an optimal thickness distribution having a total volume equal to or less than that of the initial thickness.