A variable stiffness model (VSM) of the anechoic coating is proposed to calculate the sound absorption performance under hydrostatic pressure by considering both hyperelasticity and deformation. The expression for tangent stiffness is derived based on the Mooney-Rivlin dual parameter model. A VSM algorithm is then established. For the VSM algorithm, based on the hyperelastic constitutive equation, the equivalent modulus matrix of the material and the tangent stiffness matrix of the structure are modified according to the stress and deformation state formed by hydrostatic pressure, and then applied to sound absorption calculations. The results obtained by the VSM algorithm are consistent with the experimental data reported in the literature. We find that hydrostatic pressure can cause anisotropic behavior in hyperelastic materials, and then reveal the underlying mechanisms by which hydrostatic pressure weakens the sound absorption performance of anechoic coatings in terms of geometric deformation and hyperelastic properties. This study provides a scientific basis for developing highly efficient anechoic coatings in conditions of high hydrostatic pressure, which has significant theoretical and engineering application value. It contributes to the advancement of new underwater anechoic coating technologies.