We investigate the equilibrium lattice constant, bulk modulus, elastic constants and Debye temperature of Li2 O under pressure by using ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The obtained results at zero pressure are well consistent with the available experimental data and other theoretical results. It is found that the elastic constants C11, C12 and C44 and bulk modulus B increase monotonously as pressure increases. Also, the anisotropy will weaken and the Debye temperature will rise with pressure increasing.