Most numerical codes modeling wave propagation for seismic imaging are based on isotropic elastodynamic equations. These equations are not appropriate to model complex geophysical media and, to perform more realistic simulations, it is necessary to take into account the anisotropy of the media. Therefore numerical methods should now be adapted to Vertical Transverse Isotropy (VTI) and Tilted Transverse Isotropy (TTI). This extension increases dramatically the number of parameters to be stored in each cell of the mesh and we need to develop efficient techniques to reduce the computational costs. In particular, we wish to develop artificial boundary conditions to reduce the size of the computational domain. This can be done by using Absorbing Boundary Conditions (ABCs) or Perfectly Matched Layers (PMLs). However, ABCs are only adapted to homogeneous and isotropic media. On the other hand, PMLs are unstable in most TTI media. The aim of this talk is to present a new ABC modeling the propagation of anisotropic waves in heterogeneous media. Contrary to PML, this ABC can be applied on arbitrarily shaped convex boundary. Numerical results obtained by a Discontinuous Galerkin method will illustrate the performance of the condition.