When the classic compact finite difference scheme was applied to practical problems using non-uniform meshes,the spurious numerical oscillations would be excited.A high accuracy of compact scheme was developed for this problem.The general expressions of the scheme's coefficients were derived through Taylor expansion analysis;then the numerical dispersion and dissipation were analyzed by using Fourier analysis method.For the case that the sixth-order tridiagonal compact scheme was applied to non-uniform meshes,the results are shown:the dispersion and dissipation values are closer to the exact solution with the increase of disturbance factor;the scheme is asymptotically stable when the disturbance factor is less than or equal to 0.213,otherwise it is the opposite;the results of numerical solution for one-dimensional convective wave and two-dimensional wave propagation agree well with the theoretical solution,which shows advantages in the simulation of non-uniform meshes for computational aeroacoustis.