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The experimental setup is devised to simulate the presence of vertical cracks with varying widths within concrete structures. Co-polarimetric ground-penetrating radar (GPR) surveys are carried out to acquire the “VV” and “HH” polarization data. The time-varying centroid frequency attribute is employed to describe the vertical variation in the center frequency of the radar wave, unveiling a gradual vertical decay in the centroid frequency at the locations of vertical cracks. An improved time-varying centroid frequency attribute based on the adaptive sparse S-transform (ASST) is proposed and tested by a finite-difference time-domain model and co-polarimetric GPR data, which can offer better resolution compared to that of the conventional S-transform. By analyzing the waveform and centroid frequency properties of the two polarizations, we conclude that the “VV” polarization is relatively sensitive to centimeter scale cracks, while the “HH” polarization is more sensitive to millimeter scale cracks.