First, SS precursor boundary sensitivity kernel is calculated based on finite-frequency theory and the sensitivity of SS precursor traveltime perturbation to the topography perturbation implemented on mantle discontinuity is analysed. Next, SS precursor waveform with topography perturbation implemented on mantle discontinuity is simulated using SPECFEM and its traveltime perturbation is measured and compared with the traveltime perturbation predicted by finite-frequency theory. It is found that finite-frequency theory can well explain the wavefront healing effect of SS precursor. At last, an inversion scheme is built based on boundary sensitivity kernel, and more reliable topography of the mantle discontinuity can be obtained after considering the finite-frequency effect of SS precursor. This research provides some preliminary knowledge for inversion of the topography of mantle discontinuities using SS precursor.