The crystal structure and the locations of the hydrogen of lithium imide （Li2NH） are studied by first-principle plane wave pseudopotential method based on the density function theory（DFT）. Three models are used to investigating the effects of the Li, N and nearest-neighbor N—H bonds to N—H bond orientation, respectively. The calculated results show that Li2NH crystal can be described by a layered tetragonal crystal （P42） structure. Four N—H bonds of each conventional cell align in two layers. The two imide groups in the same layer prefer to be antiparallel and the imide groups in the nearest-neighbor layers tend to be vertical. The density of states （DOS） and the electron local function （ELF） analysis show strong ionic interaction between the Li and N—H dimmer, while the bonding between the N and H has covalent character. Our P42 structure of Li2NH crystal yields a hydrogen storage Li2NH2+H2/LiNH2+LiH reaction enthalpy of 69.6 kJ/mol H2 at T=0 K, in good agreement with experimental reports of 66 kJ/mol H2 for this reaction.