Redox-active organic electrode materials have garnered considerable interest as an emerging alternative to currently widespread inorganic-(or metal)-based counterparts in lithium-ion batteries (LIBs). Practical use of these materials, however, has posed a challenge due to their electrically insulating nature, limited specific capacity, and poor electrochemical durability. Here, a new class of multiwalled-carbon-nanotube-(MWCNT)-cored, meso-tetrakis(4-carboxyphenyl) porphyrinato cobalt (CoTCPP) is demonstrated as a 1D nanohybrid (denoted as CC-nanohybrid) strategy to develop an advanced LIB anode. CoTCPP, which is one of the metalloporphyrins having multielectron redox activities, shows strong noncovalent interactions with MWCNTs due to its conjugated π-bonds, resulting in successful formation of the CC-nanohybrids. The structural uniqueness of the CC-nanohybrid facilitates electron transport and electrolyte accessibility, thereby improving their redox kinetics. Inspired by the 1D structure of the CC-nanohybrid, all-fibrous nanomat anode sheets are fabricated through concurrent electrospraying/electrospinning processes. The resulting nanomat anode sheets, driven by their 3D bicontinuous ion/electron conduction pathways, provide fast lithiation/delithiation kinetics, eventually realizing the well-distinguishable lithiation behavior of CoTCPP. Notably, the nanomat anode sheets exhibit exceptional electrochemical performance (≈226 mAh g sheet −1 and >1500 cycles at 5 C) and mechanical flexibility that lie far beyond those achievable with conventional LIB anode technologies.