A first-principles method is applied to comparatively study the stability of lithium metal oxides with layered or spinel structures to predict the most energetically favorable structure for different compositions. The binding and reaction energies of the real or virtual layered LiMO₂ and spinel LiM₂O₄ (M=Sc-Cu, Y-Ag, Mg-Sr, and Al-In) are calculated. The effect of element M on the structural stability, especially in the case of multiple-cation compounds, is discussed herein. The calculation results indicate that the phase stability depends on both the binding and reaction energies. The oxidation state of element M also plays a role in determining the dominant structure, i.e., layered or spinel phase. Moreover, calculation-based theoretical predictions of the phase stability of the doped materials agree with the previously reported experimental data.