Based on the density functional theory (DFT) and full-potential linearized augmented plane wave (FLAPW) method, the hydrogen occupied sites, electron densities and densities of states were analyzed for the solid solution phase α-LaNi4.5Al0.5H0.5 and α-LaNi4.5Al0.5H1.0. The hydrogen atom in α-LaNi4.5Al0.5H0.5 is found to prefer the 6 m position near aluminum atom, the two hydrogen atoms in α-LaNL4.5Al0.5 H0.5H1.0 are most likely to take the 6m and 4 h* sites by total energy minimization calculation. The lattice expansion is mainly along the c axis. The interaction between aluminum and nickel, hydrogen plays a dominant role in the stability of LaNi4.5Al0.5Hx solid solution phase. The smaller the shift of EF towards higher energy region, the more stable the compounds will be. The calculated results are compared with the existent experimental data and discussed in light of previous works.