In this paper, the application of the Gaussian Kernel Smoothing Filter (GKSF) in the field of structural health monitoring (SHM) for bridges is explored. A baseline-free, GKSF-based method is developed to detect and localize structural damage in bridges subjected to truckloads. The study reveals that an adjusted GKSF can effectively smooth acceleration responses, where the smoothed response is dominated by the first natural frequency of the bridge. By employing a damage index (DI) based on the normalized energy of the smoothed acceleration signal, the method successfully identifies both the location and severity of structural damage in bridge structures. To validate the proposed approach, a simply supported bridge under a moving sprung mass is numerically modeled, and acceleration responses are obtained along the bridge’s length. The results indicate that the method is capable of accurately identifying the location and severity of structural damage, even in noisy environments. Notably, since the method does not require the determination or monitoring of dynamic modal parameters, it is classified as a baseline-free and rapid damage detection technique.