The basic physical properties of the layered lithium manganese oxide Li₂MnO₃ and the spinel lithium manganese oxide LiMn₂O₄ were investigated by the first-principles calculations based on density functional theory in this paper. Herein, the differences in crystal structures, electronic structures, and Li-ion transport characteristics between Li₂MnO₃ and LiMn₂O₄ were discussed in detail. It was found that both Li₂MnO₃ and LiMn₂O₄ are semiconductors, but the band gap of Li₂MnO₃ (2.1 eV) is much larger than that of LiMn₂O₄ (0.36 eV). The phonon dispersions show both the anti-ferromagnetic (AFM) configurations of Li₂MnO₃ and LiMn₂O₄ are dynamically stable. Moreover, the migration of Li ions in LiMn₂O₄ is faster than that in Li₂MnO₃. To further increase the Li diffusivity of Li₂MnO₃, the tetravalent dopants (Ir⁴⁺, Os⁴⁺, and Ru⁴⁺) were considered to substitute the Mn site of Li₂MnO₃. Our theoretical results explain the higher stability of doped Li₂MnO₃ through enhancing the Li migrating ability.