Five compositions of Li[(CoNi1/2Mn1/2) x (Li1/3Mn2/3)(1−2x)]O2 solid solutions with layered lithium manganese oxides were designed using a triangle phase diagram and were synthesized using a sol–gel method. The phase diagram satisfied the theoretical manganese oxidation state of 4+ over the whole triangle plane of the diagram and was expressed with a design equation of Li[(CoNi1/2Mn1/2) x (Li1/3Mn2/3)(1−2x)]O2. It was found that the solid solutions were synthesized with layered structure maintaining the manganese oxidation state of 4+ and showed a one-step monotonous discharge curve shape without structural transformation to spinel during charge/discharge processes. The synthesized solid solutions delivered high discharge capacities with negligible capacity fading.