The study of phonons describes the thermodynamic properties behavior of compounds with small atoms because phonons have an important influence on its properties. Lithium borohydride, LiBH4, is one of the suitable materials for hydrogen storage solid state. Although the transformations of Lithium borohydride LiBH4 were repeatedly studied by experiments and fundamental side, these transformations are still under discussion. In the present work, the mode vibrational analysis of orthorhombic and hexagonal LiBH4 structures were considered with ab initio lattice-dynamics based on the quasi-harmonic approximation approach as implemented in Phonopy code. The results show that the orthorhombic structure is thermodynamically stable, while the hexagonal structure is unstable owing to the presence of negative mode frequency. The thermal expansion behavior and various thermodynamic properties stability like heat capacity, entropy and Helmholtz energy were also studied and the obtained results are in good agreement with experiments. This shows a deep connection between stability and strength and helps researchers to estimate accurately the thermodynamic performance of LiBH4 materials. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.