Using ab initio density functional theory calculations, the electron localization function (ELF) of typical transition metal carbide TiC and nitride TiN were computed and analyzed to reveal their nature of the chemical bonds. The ELF approach was initially validated through typical examples of covalent-bonding Diamond (C) and ionic-bonding sodium chloride NaCl. Our results clearly demonstrate the dominantly ionic bonding characteristics of TiC and TiN. It is also suggested that the high mechanical hardness of TiC and TiN can be explained without evoking strong covalence.