With the importance of the fractured strata in the oil exploration, researchers have paid more attention to the wave propagation in viscoelastic and anisotropic media. Provided the rocks are weakly viscoelastic, the viscoelastic problems can be solved as a series of elastic problems by using the time increment method. At each step we determine the viscoelastic deformations and the corresponding viscoelastic loads, which are added to the load vectors for the next step. On this basis, the finite-element recursive formulae of viscoelastic and azimuthally anisotropic media are established. The numerical simulations show the characteristics of wavefields in the viscoelastic and azimuthally anisotropic media.