Pseudospectral Method is one of the methods to solve the partial differential equations numerically. Pseudospectral methods involve the expansion of the solution to a differential equation in high-order orthogonal expansion, the coefficients of which are determined by a weighted-residual projection technique. The main attraction of pseudospectral method is accuracy; however complex flow problems are typically difficult to solve. Several problems in practical solution of pseudospectral method for atmospheric diffusion equation are considered. The accuracy of Fourier expansion and Chebyshev expansion methods, FFT (Fast Fourier Transform) algorithm, the treatment of boundary condition and Gibbs phenomenon etc. are discussed, and the results of pseudospectral solution are compared with the results of analytical solution at steady state.