A Pd nanoshell was epitaxially grown on a Au nanorod (NR) via simple seed-mediated growth. Compared with the cylindrical shape of the Au NR, the Au core/Pd shell (Au@Pd) nanorods change to a rectangular shape due to the disappearance of {110} facets. The Au NRs exhibit a strong longitudinal surface plasmon resonance (LSPR). As Pd is deposited, damping and broadening occur to the LSPR band. Interestingly, the LSPR band maximum first shows a small red-shift (ca. 40 nm) which then is followed by a blue-shift as the amount of Pd is increased. A thickness-dependent LSPR feature of the Pd shell is believed to contribute to the shift. At a thinner Pd thickness, the Au@Pd nanobars exhibit a well-defined LSPR band in the visible and near-infrared region, which demonstrates a higher dielectric sensitivity than that of the corresponding Au NRs. It thus opens up the potential of Pd nanostructures for SPR-based sensing. Investigations on the surface-enhanced Raman scattering (SERS) indicate that the SERS activities of the Au@Pd nanobars at thicknesses smaller than 2.5 nm mainly originate from the Au cores; thus, the SERS activities can be improved by tuning the aspect ratio of the Au core and/or the Pd shell thickness.