Drilled boreholes are commonly used to detect rock voids and fractures in underground construction projects such as pile foundations, tunnel borings, and other near surface human activities. However, voids can be missed by direct drilling due to their limited size. Borehole sonic sounding can be used to image voids in the vicinity of the borehole. We developed a new time domain full-waveform inversion method for borehole sounding data. The FWI method employ an amplitude envelope-based objective function which captures low-frequency components to provide the initial velocity model for further inversion. Then a global correlation-based objective function is applied for FWI based on the updated initial velocity model. Numerical studies show that modeled anomalies of a single void, multiple voids and fractures are successfully delineated by the inverted Vs velocity profile. The FWI method was applied to field data from a bridge foundation project in a karst area and compared to complementary cross-hole acoustic tomography borehole profiles and drilled corehole data. The single borehole FWI inverted velocity profiles identify voids in agreement with the cross hole tomography and corehole observations. The results demonstrate that FWI is capable of imaging karst voids near drilling boreholes using borehole sonic data.