Sulfur is a prospective material for next-generation batteries with high theoretical capacity, but its drawbacks hinder its commercialization. To overcome the low conductivity of natural sulfur and the shuttle effect of lithium polysulfide, the study proposes a novel sulfur film coated with three-dimensional nitrogen and cobalt-codoped polyhedral carbon wrapped on a multiwalled carbon nanotube sponge (3D-S@NCoCPC sponge) composite as a high-performance cathode material for rechargeable lithium-sulfur batteries. The interconnected conductive carbon network with abundant pores provides more room for the homogeneous distribution of sulfur within the composite and creates a favorable pathway for electrolyte permeability and lithium-ion diffusion. Moreover, the strong interaction between cobalt and lithium polysulfides leads to efficient suppression of the shuttle effect. In addition, the homogeneous distribution of sulfur and cobalt within the composite enhances electronic transfer for the conversion reaction of sulfur. As expected, the cathode with a high sulfur content of 77.5 wt % in the composite achieved a high initial discharge capacity of 1192 mA h g-1 and high Coulombic efficiency of 99.98% after 100 cycles at 100 mA g-1 current density. Stable performance was achieved with 92.9% capacity retention after 200 cycles at 1000 mA/g current density.