Detail analyzes to the electronic structure of magnesium based ternary metal hydrides containing alkali and alkaline-earth elements (R-CsMgH3) is reported so as to justify its use as advanced hydrogen storage systems. Calculations based on full-potential method within several exchange correlation potentials are performed to gain a reliable results. It has been found that alpha-CsMgH3 exhibits indirect band gap of about 2.3 eV (local density approximation-LDA), 2.6 eV (generalized gradient approximation-PBE-GGA), 2.9 eV (Engel-Vosko generalized gradient approximation - EVGGA) and 3.2 eV (recently modified Becke-Johnson potential -mBJ). The electronic band structure and the density of states reveal that at the energy regions around 5.0 eV and from 3.5 eV up to 2.0 eV the H-1s state hybridized with Mg-3s state to form a peak at around 5.0 eV and three peaks between 3.5 eV and 2.0 eV. The energy region from 2.0 eV up to Fermi level is originated by the interactions between H-1s and Mg-2p states. Thus, the interactions between the orbitals of H and Mg atoms leads to form strong covalent bonding between H and Mg atoms. The conduction bands are mainly originated from the empty states of Cs and partially from Mg-3s/2p states, while H-1s has insignificant contribution to the empty states. The chemical bonding were analyzed in term of charge density and charge transfer, we found that a charge transfer towards H atom occur. To gain further insight for deeply understanding the electronic structure, the optical dielectric functions are calculated based on the calculated band structure. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.