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The stability, electronic structure, elasticity, and heat capacity of titanium borides were calculated by first-principles density functional theory. The results show that TiB with the space group of and are unstable, and the most stable stucture belongs to TiB2. All of the borides show a mixed character of metallic, covalent and ionic bonds, Ti2B shows high metallic property, while TiB2 has high level of covalent bonding. The values of bulk moduli, shear moduli and Young’s moduli are 251.4, 260.1 and 564.6 GPa, respectively, which are obviously higher than that of other borides. The calculated B/G values clearly imply that TiB2 is more brittle than other borides. The brittle nature of TiB2 (B/G=0.97) constrains its application as potential cutting tools or wear resistant parts. Thus TiB2-based composites should be designed in order to improve the ductile property. Finally, the anisotropy index and heat capacity of the titanium borides were also predicted