We demonstrate the morphology and spectral properties of silver-coated gold nanorods (AuNRs@Ag), synthesized via seed-mediated growth, using scanning electron microscopy (SEM) and dark-field (DF) spectroscopy. The relationship between surface damping and the thickness of the Ag shell in AuNRs was analyzed at the single-particle level. Additionally, we adjusted the bulk damping and radiation damping of AuNRs to elucidate the contribution of surface damping. SEM images demonstrated an increase in length and width following Ag deposition. Elemental mapping analysis confirmed the Ag deposition on the AuNR surface, with Ag content measured at 26.7% for AuNR@Ag26.7 with a 1-day incubation period and 34.8% for AuNR@Ag34.8 with a 2-day incubation period. DF spectroscopy revealed a notable blue shift and slight broadening in their LSPR spectra. Moreover, surface damping decreased with an increase in Ag content. Consequently, this study advances the understanding of plasmon damping mechanisms in single AuNR@Ag for their potential applications.