According to the plane wave pseudo-potential method of the first-principles based on density functional theory, we systematically investigate the cell parameters, the formation heat and the reaction enthalpy in the Li-N-H hydrogen storage process. The calculated lattice parameters of these compounds are in good agreement with previous theoretical and experimental results. The values of formation heat at 298 K for (lithium nitride) Li3N, (lithium hydride) LiH, (lithium amide) LiNH2 and (lithium imide) Li2NH are estimated to be -168.7, -81.0, -173.0 and -190.8 kJ/mol, respectively. The reaction enthalpy of this system is calculated to be 78.5 kJ/mol H2 at T=298 K and this value accords with the experimental value of 75.67 kJ/mol H2 at T=300 K. As a result, the reaction enthalpies for the two-step reactions are very close to their calculation results respectively.