Nano-sized cathode materials for high power lithium ion polymer battery are easily and economically prepared using united eutectic self-mixing method without any artificial mixing procedures of reactants and ultra-miniaturization of products. While the micro-sized $LiNi_{0.7}Co_{0.3}O_2$ exhibits the discharge capacities of 167.8 mAh/g at 0.1C and 142.5 mAh/g at 3.0C, those of the nano-sized $LiNi_{0.7}Co_{0.3}O_2$ are 170.8 mAh/g at 0.1C and 159.3 mAh/g at 3.0C. In the case of $LiCoO_2$, the micro-sized $LiCoO_2$ exhibits the discharge capacities of 134.8 mAh/g at 0.1C and 118.6 mAh/g at 5.0C. Differently, the nano-sized $LiCoO_2$ exhibits the discharge capacities of 137.2 mAh/g at 0.1C and 131.7 mAh/g at 5.0C.