We have developed a new approach for acoustic wave modeling in transversely isotropic media with a vertical axis of symmetry. This approach is based on using a pure acoustic wave equation derived from the basic physical laws — Hooke’s law and the equation of motion. We find that the conventional equation noted as a pure quasi-P-wave equation computes only one stress component. In our approach, there is no need to approximate the pseudodifferential operator for decomposition purposes. We make a discrete inverse Fourier transform of the desired frequency response contained in the pseudodifferential operator to build the corresponding spatial operator. We then cut off the operator with a window to reduce edge effects. As a result, the obtained spatial operator is applied locally to the wavefield through a simple convolution. Consequently, we derive an explicit numerical scheme for a pure quasi-P-wave mode. The most important advantage of our method lies in its locality, which means that our spatial operator can be applied in any selected region separately. Our approach can be combined with classical fast finite-difference methods when media are isotropic or elliptically anisotropic, therefore avoiding spurious fields and reducing the total computational time and memory. The accuracy, stability, and absence of residual S-waves of our approach were proven with several numerical examples.