The ordered heterogeneity much smaller than the wavelength will results in velocity anisotropy and thus affects the kinematic and dynamic properties of the seismic waves. As the tools to describe the wave propagation in earth's media, anisotropic elastic wave equations play key roles in seismic modeling, migration and inversion. To generate flexible and efficient wave propagators in anisotropic media for practical usage, people never give up to construct simplified anisotropic wave equations in the past years. In this paper, based on wave-mode separation theory, we propose so called pseudo-pure P-wave equations which are equivalent to the original elastic wave equation in kinematics but highlight the P-wave energy. We derive the pseudo-pure P-wave equations in TI media and their further simplified forms. The examples of synthesized wavefront snapshots and reverse time migration prove that, the pseudo-pure-mode wave equation is accurate anisotropic wave propagator with distinguishing features, and has great potential in seismic modeling, imaging and parameter inversion.