Provided is a cathode composition for lithium secondary battery that includes a lithium-chromium-titanium-manganese oxide that has the formula Li[Li.sub.(1-x)/3Cr.sub.xTi.sub.(2/3)yMn.sub.2(1-x-y)/3]O.sub.2 where 0.ltoreq.x.ltoreq.0.3, 0.ltoreq.y.ltoreq.0.3 and 0.1.ltoreq.x+y.ltoreq.0.3, and layered a-LiFeO.sub.2 structure. A method of synthesizing the lithium-chromium-titanium manganese oxide includes preparing a first mixed solution by dispersing titanium dioxide (TiO.sub.2) in a mixed solution of chrome acetate (Cr.sub.3(OH).sub.2(CH.sub.3CO.sub.2).sub.7) and manganese acetate ((CH.sub.3CO.sub.2).sub.2Mn.4H.sub.2O), adding a lithium hydroxide (LiOH) solution to the first mixed solution to obtain homogeneous precipitates, forming precursor powder that has the formula Li[Li.sub.(1-x)/3Cr.sub.xTi.sub.(2/3)yMn.sub.2(1-x-y)/3]O.sub.2 where 0.ltoreq.x.ltoreq.0.3, 0.ltoreq.y.ltoreq.0.3 and 0.1.ltoreq.x+y.ltoreq.0.3 by heating the homogeneous precipitates, and heating the precursor powder to form oxide powder having a layered structure.