[ $Li[Co_{0.50}Li_{0.17}Mn_{0.33}]O_2$ ] powder was prepared using a simple combustion method. specially, ratio of 2:1, 3:2, 1:1, 2:3, 1:2 was adopted as acetate source/nitrate source. The diffraction pattern of $Li[Co_{0.50}Li_{0.17}Mn_{0.33}]O_2$ powder showed that this compound could be classified as hexagonal $a-NaFeO_2$ structure (space group : $Rar{3}m$). The size of powder was less than $1{mu}m$. Small particle size of cathode powder would give a good ionic and electronic conductivity to cathode electrode, which made of cathode powder. As the increase of nitrate source-ratio, discharge capacity of $Li[Co_{0.50}Li_{0.17}Mn_{0.33}]O_2$ at high charge-discharge rate was increased. When the ratio of acetate source/nitrate source was 1:2, discharge capacity at 10 C rate (2000 mA/g) was 180 mAh/g. It was $10{sim}15%$ larger than that of powder, which have 2:1 as acetate source/nitrate ratio.