Seismic anisotropy has become a main research topic in both seismic data processing and interpretation (e.g., migration and impedance inversion). As an important part of seismic anisotropy, numerical modeling can help us better understand seismic responses when seismic waves propagate through the interior of the Earth. For the numerical implementation of finite-difference time-domain algorithms, boundary conditions are needed to suppress the spurious reflections from the artificially truncated edges of the discrete model. Here, the nearly perfectly matched layer (NPML) technique is applied to a numerical simulation of seismic-wave propagation in a 2D elastic anisotropic medium, which has been proven to be a very effective absorbing boundary condition in electromagnetic, acoustic, and elastic isotropic media. The equivalence of the wave absorbing performance between the NPML and the standard perfectly matched layer (PML) for elastic wave modeling is theoretically proven in this paper. To check the absorbing ability of the NPML in the cases of grazing incidence and longer simulations (up to 200 s), we choose an elongated anisotropic model in our test. Test results indicate that the NPML has essentially the same computational accuracy as the standard PML but with higher computational savings.