In this article, under the assumption of weak anisotropy and weak attenuation, we present approximate solutions of anisotropic complex velocities and quality-factors for Kelvin visco-elastic transverse isotropy (KEL-VTI) media, based on the complex physical parameter matrix. Also, combined with the KEL-VTI media model, the propagation characteristics of the qP-, qSV-, and qSH-wave phases and energies are discussed. Further, we build a typical KEL-VTI media model of the Huainan coal mine to model the wave propagation. The numerical simulation results show that the PP-and PSV-wave theoretical wave-fields are close to the wave-fields of three-component P-and converted-waves acquired in the work area. This result proves that the KEL-VTI media model gives a good approximation to this typical coalfield seismic-geologic conditions and is helpful to the study of attenuation compensation of multi-component seismic data.