Single-walled carbon nanotubes (SWCNTs) are quasi-one-dimensional systems with poor Coulomb screening and enhanced electron-phonon interaction, and are good candidates for excitons and exciton-phonon couplings in metallic state. Here we report back scattering reflection experiments on individual metallic SWCNTs. An exciton-phonon sideband separated by 0.19 eV from the first optical transition peak is observed in a metallic SWCNT of chiral index (13,10), which provides clear evidences of excitons in metallic SWCNTs. A static dielectric constant of 10 is estimated from the reflectance spectrum.PACS numbers: 81.07.De Single-walled carbon nanotubes (SWCNTs) have been the topic of extensive research for their potentially broad applications [1] and fundamental scientific interest. SWCNTs can be either semiconducting or metallic depending on their diameters and chiral angles. One of the important and challenging issues is the possible excitons in SWCNTs. Excitons are pairs of electrons and holes bound by the attractive Coulomb interaction, and are fundamental to our understanding of optical properties of semiconductors. After a series of theoretical and experimental works, a consensus has been reached that excitons are also prominent factors in optical transitions of semiconducting SWCNTs [2,3,4,5,6].Although excitons are common in semiconductors and insulators, excitons are not expected in bulk metals because of the metallic strong Coulomb screening, which prohibits the bound state of electrons and holes in three dimensional (3D) systems. SWCNTs are quasi-1D systems with poor Coulomb screening. The relaxed bounding criteria and the much weaker screening in low dimension are in favor of the existence of excitons in metallic SWCNTs, as predicted in recent theoretical studies [7,8]. Therefore, SWCNTs provide an excellent opportunity to study the possible excitons in metallic states. In metallic SWCNTs, except for the one pair of bands that touch (or nearly touch) the Fermi surface, all pairs of bands are gapped and may form exciton-continuum manifolds [9] as in semiconducting SWCNTs. Optical measurements addressing excitons in metallic SWCNTs are challenging and only very few experiments have been reported. Very recently, Wang et al. reported absorption spectrum of an armchair metallic SWCNT with chiral index of (21,21). From the line shape of the optical transition, they identified the signature of exciton formation [10]. On the other hand, Berciaud et al. reported absorption spectrum using photothermal heterodyne detection. They found no exciton-phonon sideband and suggested weak excitonic effect in metallic SWCNTs [11]. The lack of experiments on metallic SWCNTs is partially due to the fact that photoluminescence spectroscopy, which is widely used in semiconducting SWCNTs, can not be employed in metallic systems because of their low fluorescence yield. Resonant Raman scattering is also popular, but difficult to obtain a wide-range spectrum which is usually needed to obtain the excitonic information. In contrast, R...