Li-O2 batteries have attracted considerable attention for several decades due to their high theoretical energy density (>3400 Wh/kg). However, it has not been clearly demonstrated that their actual volumetric and gravimetric energy densities are higher than those of Li-ion batteries. In previous studies, a considerable quantity of electrolyte was usually employed in preparing Li-O2 cells. In general, the electrolyte was considerably heavier than the carbon materials in the cathode, rendering the practical energy density of the Li-O2 battery lower than that of the Li-ion battery. Therefore, air cathodes with significantly smaller electrolyte quantities need to be developed to achieve a high specific energy density in Li-O2 batteries. In this study, we propose a core-shell-structured cathode material with a gel-polymer electrolyte layer covering the carbon nanotubes (CNTs). The CNTs are synthesized using the floating catalyst chemical vapor deposition method. The polymeric layer corresponding to the shell is prepared by the layer-by-layer (LbL) coating method, utilizing Li-Nafion along with PDDA-Cl [poly(diallyldimethylammonium chloride)]. Several bilayers of Li-Nafion and PDDA, on the CNT surface, are successfully prepared and characterized via X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, and thermogravimetric analysis. The porous structure of the CNTs is retained after the LbL process, as confirmed by the nitrogen adsorption-desorption profile and BJH pore-size distribution analysis. This porous structure can function as an oxygen channel for facilitating the transport of oxygen molecules for reacting with the Li ions on the cathode surface. These polymeric bilayers can provide an Li-ion pathway, after absorbing a small quantity of an ionic liquid electrolyte, 0.5 M LiTFSI EMI-TFSI [1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide]. Compared to a typical cathode, where only liquid electrolytes are employed, the total quantity of electrolyte in the cathode can be significantly reduced; thereby, the overall cell energy density can be increased. A Li-O2 battery with this core-shell-structured cathode exhibited a high energy density of approximately 390 Wh/kg, which was assessed by directly weighing all of the cell components together, including the gas diffusion layer, the interlayer [a separator containing a mixture of LiTFSI, 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (PYR-14), and PDDA-TFSI], the lithium anode, and the LbL-CNT cathode. The cycle life of the LbL-CNT-based cathode was found to be 31 cycles at a limited capacity of 500 mAh/gcarbon. Although this is not an excellent performance, it is almost 2 times better than that of a CNT cathode without a polymer coating.