The surface chemistry of carbon nanotubes is of interest for material’s processing and modification of their electronic and optical properties. Here, we present a new sulfur addition reaction to single-wall and multi-wall carbon nanotubes. Depending on the reaction conditions, we find strong evidence of addition reaction, which produces covalent bonding between sulfur atoms and the nanotube surfaces. Raman, TEM, and photoemission results are consistent with the formation of covalent S-C bonds on the sidewalls. DFT calculations also support a formation of sulfur-carbon bonding and predict electronic and vibrational states that are in good agreement with the experimental results. Based on a comparison between theory and experiments, we propose a stable episulfide (GS) grafting, which consists of of a sulfur atom bridging two carbon atoms repeated over the nanotube surface.