Power performance of lithium-ion batteries (LIBs) is generally controlled by the Li+ diffusion within crystalline framework of electrode materials, and thus nano-sized electrode materials with shortened diffusion length have been widely used to build high power LIBs. However, the undesired effects from nano-sized electrode materials, such as low tap density, low thermal stability and increased interface also discount the overall performance of LIBs. Accordingly, it is desired to develop high power LIBs with micro-sized electrode materials. Herein, we demonstrate that hard carbon displays fast Li-storage kinetics which is not controlled by Li+ diffusion in the crystalline framework. Furthermore, it is found that micro-sized spinel LiNi0.5Mn1.5O4 and LiMn2O4 have high rate performance, owing to their three-dimensional channels for Li+ diffusion. Finally, the micro-sized spinel LiNi0.5Mn1.5O4 (or Li1.1Mn2O4) and micro-sized hard carbon are used as cathode and anode, respectively, to fabricate the full cells that exhibit supercapacitor-like high power performance. The achieved results point a way to develop high power LIBs besides nano-sizing electrode materials.