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Characterizing the expressions of seismic waves in elastic anisotropic media depends on multiparameters. To reduce the complexity, decomposing the P‐mode wave from elastic seismic data is an effective way to describe the considerably accurate kinematics with fewer parameters. The acoustic approximation for transversely isotropic media is widely used to obtain P‐mode wave by setting the axial S‐wave phase velocity to zero. However, the separated pure P‐wave of this approach is coupled with undesired S‐wave in anisotropic media called S‐wave artefacts. To eliminate the S‐wave artefacts in acoustic waves for anisotropic media, we set the vertical S‐wave phase velocity as a function related to propagation directions. Then, we derive a pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis by introducing the expression of vertical S‐wave phase velocity. The differential form of new expression for pure P‐wave is reduced to second‐order by inserting the expression of S‐wave phase velocity as an auxiliary operator. The results of numerical simulation examples by finite difference illustrate the stability and accuracy of the derived pure P‐wave equation. [ABSTRACT FROM AUTHOR]