In this work, we investigated experimentally and theoretically the plasmonic Fano resonances (FRs) exhibited by core-shell nanorods composed of a gold core and a silver shell (Au@Ag NRs). The colloidal synthesis of these Au@Ag NRs produces nanostructures with rich plasmonic features, of which two different FRs are particularly interesting. The FR with spectral location at higher energies (3.7 eV) originates from the interaction between a plasmonic mode of the nanoparticle and the interband transitions of Au. In contrast, the tunable FR at lower energies (2.92-2.75 eV) is ascribed to the interaction between the dominant transversal LSPR mode of the Ag shell and the transversal plasmon mode of the Au@Ag nanostructure. The unique symmetrical morphology and FRs of these Au@Ag NRs make them promising candidates for plasmonic sensors and metamaterials components.