Accurate and efficient modeling of seismic wavefields that accounts for both attenuation and anisotropy is essential for further development of processing methods. Here, we present a 2D time-domain finite-difference algorithm for generating multicomponent data in viscoelastic transversely isotropic media with a vertical symmetry axis (VTI). Within the framework of the generalized standard linear solid (GSLS) model, the relaxation function is expressed through the -parameters (which quantify the difference between the stress and strain relaxation times) defined for anisotropic media. This approach produces nearly constant values of all components of the quality-factor matrix within a specified frequency band. The developed algorithm is based on a set of anisotropic viscoelastic wave equations parameterized by memory variables. Synthetic examples for TI models with different structural complexity confirm the accuracy of the proposed scheme and illustrate the influence of attenuation and attenuation anisotropy on multicomponent wavefields.