Here we report a novel sulfur host for Li-S batteries, a multi-functionalized core-shell carbon polyhedron (CNT-GC@NC) composite, containing graphitic carbon (GC) as the core and nitrogen-doped carbon (NC) as the shell, grafted with carbon nanotubes (CNTs) outside, which is facilely obtained through thermal treating the ZIF-67@ZIF-8 core-shell polyhedron. The unique CNT-GC@NC integrates the advantages of carbons derived from both ZIF-67 and ZIF-8 with features of hierarchically meso/microporous structure, high Co nanoparticle and N heteroatom contents and graphitic structures. It is verified that the grafting of CNTs onto the outer surface of carbon polyhedrons can form interconnected conductive networks with the highly graphitic carbon within. The embedded Co nanoparticles and doped nitrogen can synergistically promote the adsorption of sulfur species and thus the redox reaction kinetics of polysulfides. On the other hand, the nitrogen-doped and micropores-enriched NC shell acts as a physical barrier to totally enclose polysulfides within the carbon hosts. Thanks to these advantages, the CNT-GC@NC/S presents excellent rate performance and cycling stability with the high reversible capacities of 700 and 580 mAh g(-1) at 200th and 800th cycle at 1 C, respectively. (C) 2018 Elsevier B.V. All rights reserved.