When a seismic signal propagates through a realistic medium in the Earth, in add ition to anisotropy, the layers may show intrinsic viscoelastic behavior. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and viscoelastic behavior of rocks. On this basis, the pseudo spectral recursive formulae of viscoelastic and azimuthally anisotropic media are derived. Wavefield forward modeling with the pseudo-spectral method was car ried out in viscoelastic and azimuthally anisotropic media. The numerical results from the pseudo-spectral method clearly show that seismic wavefield is closely related with the viscoelasticity and the azimuth of the principal axes of anis otropy.