The stable crystal structure of LiBeH3 is predicted on the basis of ab initio total-energy calculations using density-functional theory and an extended database of candidate structures and using global optimizations based on an evolutionary algorithm. At the level of density-functional theory, a CaSiO3 -1 -type structure with space group P21 /c, containing BeH4 tetrahedra linked in chains, is the ground-state structure of LiBeH3 (α -LiBeH3). It is found to be lower in energy than the structures proposed in previous studies. The analysis of the electronic structure shows that α -LiBeH3 is an insulator with a band gap of about 4.84 eV and exhibits strong covalent bonding in the BeH4 tetrahedral complexes. Calculations at finite temperatures and high pressures suggest that at T=408 K and ambient pressure a structural transition from α -LiBeH3 (CaSiO3 -type) to a YBO3 -type structure with space group Cmcm occurs and that at a pressure of 7.1 GPa α -LiBeH3 undergoes a pressure-induced structural transition from the α -phase to a MgSiO3 -type structure with space group C2/c. The calculated enthalpies of formation (-45.36 and -30.12 kJ/mol H3 without and with zero-point energy corrections) are in good agreement with the experimental result, indicating that LiBeH3 is a potential hydrogen storage material with low activation barriers for hydrogen desorption.