A systematic calculation has been performed in order to study phase transitions and hydrogen storage properties of ternary hydride Li2MgH4 under pressure. The structural, elastic, electronic and vibrational properties of Li2MgH4 are collected by means of density functional theory. There are three phases identified; Pbam at 0 GPa, Pnma at 5 GPa and Pna2(1) at 65 GPa Pbam and Pnma phases of Li2MgH4 are found to be mechanically and dynamically stable. Ductility of the phases are determined based on Pugh's criteria. It is found that Li2MgH4 becomes ductile at 5 GPa, otherwise it is a brittle material. Electronic band structures and corresponding partial density of states of phases are also obtained. All phases at 0 GPa, 5 GPa and 65 GPa have wide band gaps, indicating that Li2MgH4 is an insulator at all pressures. The phonon dispersion curves of Pbam and Pnma phases have no imaginary frequency indicating that both phases of Li2MgH4 are dynamically stable. The gravimetric hydrogen density of Li2MgH4 is calculated as 10.52 wt %, which is a great rate along with the hydrogen desorption temperature of 670 K. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.