The absorption (anelastic attenuation) and anisotropy properties of subsurface media jointly affect the seismic wave propagation and the quality of migration imaging. Anisotropic viscoelastic model can effectively describe seismic velocity and attenuation anisotropy effects. To reduce the computational cost and complexity of elastic wave modes decoupling for seismic imaging in anisotropic attenuating media, we have developed a pure-viscoacoustic transversely isotropic (TI) wave equation starting from the complex-valued velocity dispersion relation of quasi-compressional (qP) wave. The wave equation involving fractional Laplacians has advantages of being able to describe the constant- Q (frequency-independent quality factor) attenuation, arbitrary TI velocity and attenuation, decoupled amplitude loss and velocity dispersion effects. Numerical analyses showed that the simplified equation can accurately hold the velocity and attenuation anisotropy of qP-wave in viscoelastic anisotropic media in the range of moderate anisotropy. Compared to previous pseudo-viscoacoustic equations, the pure-viscoacoustic equation can be completely free from undesirable S-wave artifacts and behaves good numerical stability in tilted transversely isotropic (TTI) attenuating media. There are obvious wavefield differences between isotropic attenuation and anisotropic attenuation cases especially in the direction perpendicular to the axis of symmetry. Furthermore, to mitigate the influences of velocity and attenuation anisotropy on migrated seismic images, we have developed an anisotropic attenuation ( Q ) compensated reverse time migration (AQ-RTM) approach based on the new propagator. The compensation can be implemented by reversing the sign of the dissipation terms and keeping the dispersion terms unchanged during wavefields extrapolation. Synthetic example from a Graben model illustrated that the anisotropic Q -compensated RTM scheme can produce images with more balanced amplitude and accurate position of reflecters compared with conventional RTM methods under assumptions of acoustic anisotropic (uncompensated) and isotropic attenuating media. Results from a Marmousi-II model demonstrated that the new methodology is applicable for complicated geological model to significantly improve imaging resolution of the target area and deep layers.