A great deal attention has recently been focused on the Li-rich solid-solution layered oxide cathode material Li₂MnO₃-LiMO₂ (LLO, M = Co, Ni, etc.), which exhibits a discharge capacity of more than 200 mAhg^-1 when operated above 4.6 V for lithium ion battery. In this study, in order to find the optimal composition of the LLO exhibiting high cathode performance, which are composed of Li₂MnO₃, LiCo_1/3Ni_1/3Mn_1/3O₂ (or LiCoO₂, LiNiO₂) and LiNi_0.5Mn_0.5O₂, the selected 120 samples having different composition were synthesized under identical preparation conditions and the dependence of the performance of the cathode material on the percentages of Li₂MnO₃, LiCo_1/3Ni_1/3Mn_1/3O₂ (or LiCoO₂, LiNiO₂) and LiNi_0.5Mn_0.5O₂ in the LLO samples was examined under same experimental conditions in the viewpoint of discharge capacity, retention of discharge capacity, average discharge voltage, energy density and rate capability. In each viewpoint, using ternary phase diagrams, the dependence of each property on the percentages of Li₂MnO₃, LiCo_1/3Ni_1/3Mn_1/3O₂ and LiNi_0.5Mn_0.5O₂ in the LLO samples was evaluated. Based on the results obtained, it was comprehensively concluded that Li[Ni_0.208Li_0.183Co_0.033Mn_0.575]O₂ (55% Li₂MnO₃-35% LiNi_1/2Mn_1/2O₂-10% LiNi_1/3Co_1/3Mn_1/3O₂) possesses the best composition as cathode material for LIBs among the testes 120 samples. In addition, the synthesis condition of Li[Ni_0.208Li_0.183Co_0.033Mn_0.575]O₂ was examined more in the viewpoint of annealing temperature.