This paper applied the modified Fourier series method to investigate the sound-vibration characteristics by establishing a composite laminated thin sector plate-cavity coupled model for the first time based on the classical plate theory (CPT) and Rayleigh-Ritz energy technique. The coupled system consists of an annular sector or circular sector plate backed by an acoustic cavity filled with air or water. Ignoring the influence of boundary conditions, displacements admissible functions of laminated sector plate and sound pressure admissible functions of cavity can be set up as a Fourier series superposition, whose composition are the superposition of Fourier cosine series and supplementary functions. The addition of these supplementary polynomials can effectively eliminate the discontinuity or jump phenomenon on the boundary. The correctness of the established analytical model has been validated by being compared with the results achieved by the finite element method (FEM). On this basis, the coupling mechanism of the weakly coupled system and the strongly coupled system are discussed in detail. In addition, some new results and discussions are given, including the cavity depth, plate thickness, anisotropic degree, varying boundary conditions and so on, which could provide reference for future research.