A Fourier pseudospectral time-domain method can be applied to wave propagation problems pertinent to computational aeroacoustics. The original algorithm of the Fourier pseudo spectral time domain method works for periodical problems without the interaction with physical boundaries. A slip wall boundary condition, combined with buffer zone technique to solve some non-periodical aeroacoustic problems has been proposed. Compared to other computational methods, pseudospectral method is preferred for its high-order accuracy.