We report a simple synthesis of Au-Ag core-shell nanorods (NRs) under alkaline conditions (pH 8.0-10.0) from silver and ascorbate ions using gold nanorods (GNRs) as the seeds. The silver ions that are reduced by the ascorbate ions become deposited on the surfaces of the GNRs to form differently dumbbell-shaped Au-Ag core-shell NRs and nanoparticles, depending on the pH and the concentration of silver ions. The longitudinal plasmon absorbance bands of the Au-Ag core-shell NRs are stronger and appear at shorter wavelengths than those for the original GNRs. We confirmed the formation of Au-Ag core-shell NRs by both energy-dispersive X-ray spectrometry and inductively coupled plasma mass spectrometry measurements, which indicate that the Ag-109/Au-197 ratios are 0.046, 0.085, and 0.097 at pH 8.0, 9.0, and 10.0, respectively. The transmission electron microscopy measurements show that the Au-Ag core-shell NRs are monodispersed (>90%).