When the cohesive energy of LiH is calculated, the many-body correlation effect between ions and the contraction of ionic orbital are included, as two separate physical mechanisms in the total energy formula. The exchange-energy between electronic orbitals is directly computed without any adjustable parameters introduced. The results showed that many-body exchange-correlation effects markedly influence the properties at zero pressure and under high pressures. When the contributions of the nearest and next-nearest ions were taken into account, the results of the isothermal equation of state is in good agreement with experimental data in the pressure range of 0—90 GPa.