  We present the structural, electronic and superconducting properties of Li2B2
under pressure within the framework of the density functional theory. The
structural parameters, electronic band structure, phonon frequency of the E2g
phonon mode and superconducting critical temperature Tc were calculated for
pressures up to 20 GPa. We predicted that the superconducting critical
temperature of Li2B2 is about 11 K and this decreases as pressure increases. We
found that even though the lattice dynamics of the E2g phonon mode is similar
to MgB2, the reduction of the {\sigma}-band density of states at Fermi level
and the raising of the E2g phonon frequency with pressure were determinant to
decrease {\lambda} and consequently Tc.
