We systematically investigate the equilibrium energy, the density of states, and the elastic property of solid CO2 by the plane wave pseudo-potential method in the generalized gradient approximation and local density approximation based on the density function theory. The calculated lattice parameters of α-quartz are consistent with other calculation values. The equilibrium energy calculation indicates that β-cristobalite structure is more stable under the ambient condition, which is consistent with the results reported in other reffrences.The computation results of elastic constants show that they are elastically stable in structure exception for stishovite and cubic-pyrite. The hardness values for these structures are evaluated according to the intrinsic hardness calculation theory of covalent crystal based on the Mulliken overlap population. The results indicate that none of these phases are of superhard material. Furthermore, we clarify the stereochemical effect of the lone-pair electrons on the hardness of the solid CO2.