To derive a totally S-wave free acoustic approximation, we propose a new acoustic approximation for pure P-waves that is totally free of S-wave artifacts in the homogenous VTI model. To keep the S-wave velocity equal to zero, we formulate the vertical S-wave velocity to be a function of the model parameters, rather than simply setting it to zero. Then, the corresponding P-wave phase and group velocities for the new acoustic approximation are derived. For this new acoustic approximation, the kinematics is described by a new eikonal equation for pure P-wave propagation, which defines the new vertical slowness for the P-waves. The accuracy of our new P-wave acoustic approximation is tested on numerical examples. We find that the accuracy of our new acoustic approximation is as good as the original one for the traveltime and the relative geometrical spreading. Therefore, the S-wave-free acoustic approximation could be further applied in seismic processing that requires pure P-wave data.