Acoustic analysis plays significant role in engineering calculations such as noise control and indoor sound insulation. Since the practical acoustic problems usually involve sound-absorbing materials, it is very necessary to analyze acoustic problems with impedance boundary conditions. The generalized finite difference method is a new mesh-less numerical discretization method, this method is based on Taylor series expansion of multivariate function and weighted least square, the partial derivatives of unknown values in the governing equation are expressed as a linear combination of function values at supporting nodes. In this paper, the generalized finite difference method is applied to the analysis of cavity acoustics with impedance boundary conditions firstly, and the corresponding numerical discrete scheme is established. Compared with traditional algorithms, the developed numerical model is a local meshless method with the merits of being mathematically simple, numerically accurate and easy to large-scale acoustic analysis. A benchmark numerical example with analytical solution is examined to verify the influence of the total number of nodes and the number of local supporting nodes on the numerical results, and to obtain an empirical formula of the relationship between maximum computable frequency and node spacing. In addition, the generalized finite difference method is applied to two-dimensional and three-dimensional complex acoustic models without analytical solutions, and is compared with the FEM solutions obtained by COMSOL Multiphysics. Numerical experiments demonstrate that the generalized finite difference method is an efficient, accurate, stable and convergent numerical method, and has broad application prospects in the acoustic analysis of cavities with impedance boundaries.