The structural characteristic and elastic property of ReB2 in P63/mmc structure (hP6-ReB2) were computed using the pseudopotential plane-wave methods based on the density functional theory. The equilibrium structural parameters of hP6-ReB2 were calculated and its stability was verified thermodynamically, dynamically, and mechanically. It is found that the elastic constants, aggregate moduli increase as the pressure increases, and the Poisson ratio σ of hP6-ReB2structure shows its brittleness, and the elastic waves reveals its elastic anisotropy. In addition, the obtained Vickers hardness of hP6-ReB2 is 38.2 GPa. The density of electronic states reveals that there is a strong covalent bond between Re-B and B-B of hP6-ReB2, and the covalent bond increases gradually with the increase of pressure.