Based on the first-principles plane-wave basis pseudopotential calculations, we investigate mechanical properties and electronic structures of the hardest known oxide, cotunnite TiO2.The calculated results show that cotunnite TiO2 has the highest bulk modulus (348 GPa) and hardness (32 GPa) among the high-pressure phases of TiO2, but its mechanical properties are not superior to those of c-BN.Moreover, the high hardness of cotunnite TiO2 can be understood from both the dense crystal structure (high valence electron density and short bond lengths) and the unusual mixtures of covalent and ionic bonding of Ti-O.