The use of subdivision surface overcomes the difficulty of the gap in the surface slice splicing of NURBS, and can construct the smooth and continuous overall surfaces with arbitrary free-form topology. In the acoustic field, the higher the frequency, the shorter the wavelength and the larger the number of meshes to meet the calculation accuracy required. The traditional methods require reconstruct the mesh of the original structure model, which takes a lot of time. A subdivision surface method only requires refinement operation of the initial discrete mesh, which can provide multi-level-resolution control grid to avoid complex and time-consuming pre-processing. Combining the Catmull-Clark subdivision surface with the boundary element method, the interpolation approximation of geometry and physical field was carried out by using the high-order bi-cubic B-spline basis function, which not only provides the result of higher calculation accuracy, but also satisfies the requirement of broadband mesh. For the acoustic scattering problem of the structure of the adhesive sound absorbing material, the acoustic impedance boundary condition was introduced. The mathematical optimization model was established, which takes the density of the sound absorbing material element as the design variable and the volume fraction of the sound absorbing material as the constraint. The sensitivity of the objective function to the design variables was calculated by using the adjoint variable method, and the design variables were updated by the method of moving asymptotes. Finally the optimal distribution of sound absorbing materials was obtained. The correctness and validity of the algorithm were verified.