The optimal nearly-analytic discrete (ONAD) method is a new numerical method developed in recent years for solving the wave equation. Compared with other methods, such as popularly-used finite-difference methods, the ONAD method can effectively suppress the numerical dispersion when coarse grids are used. In this paper, the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates. To investigate the accuracy and the efficiency of the ONAD method, we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model. The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion, small memory requirement for computer codes, and fast calculation. As an application, we use the ONAD method to simulate the SH-wave propagating between the Earth’s surface and the core-mantle boundary (CMB). Meanwhile, we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.