The structural, anisotropic elastic properties and the ideal compressive and tensile strengths of titanium diboride (TiB2) were investigated using first-principles calculations based on density functional theory. The stress–strain relation-ships of TiB2 under , , and compressive loads were calculated. Our results showed that the ideal uniaxial compressive strengths are|σ|=142.96 GPa,|σ|=188.75 GPa, and|σ|=245.33 GPa, at strains?0.16,?0.32, and?0.24, respectively. The variational trend is just the opposite to that of the ideal tensile strength withσ=44.13 GPa, σ=47.03 GPa, andσ=56.09 GPa, at strains 0.14, 0.28, and 0.22, respectively. Fur-thermore, it was found that TiB2 is much stronger under compression than in tension. The ratios of the ideal compressive to tensile strengths are 5.56, 2.55, and 4.01 for crystallographic directions,, and, respectively. The present results are in excellent agreement with the most recent experimental data and should be helpful to the understanding of the compressive property of TiB2.