Discrete-variational(DV)-$X{alpha}$ method was applied to investigate the electronic structures of spinel- type manganese oxide which is well known to the high performance adsorbent or cathode material for lithium ion. The results of DOS(density of states) and Mulliken population analysis showed that Li was nearly fully ionized and interactions between Mn and O were strong covalent bond. The effective charge of Li and Mn was +0.77 and +1.44 respectively and the overlap population between Mn and O was 0.252 in $LiMn_2O_4$. These results from DV-X$alpha$ method were well coincided with the experimental result by XPS analysis and supported the feasibility of theoretical interpretation for the $LiMn_2O_4$ compound.