The lithium-sulfur (Li-S) battery faces a couple of major problems in practical applications, including the low conductivity of sulfur and the dissolution of polysulfides. A cathode constructed using a composite of sulfur and ordered mesoporous carbon (OMC) is a promising solution to both problems, as OMCs can have high conductivity and a complex pore structure to trap polysulfides. In this work, we demonstrate that performance of the Li-S battery can be significantly enhanced by using an OMC with a high degree of graphitization and a pore network with cubic symmetry. This graphitic OMC (GOMC) can be produced in a single step using iron phthalocyanine precursor and a silica template with cubic Ia3d symmetry. The GOMC-sulfur (GOMC/S) composite is 175% higher in electrical conductivity compared to the typical OMC-sulfur (OMC/S) composite. In addition, the three-dimensional pore network in GOMC prevents the migration of dissolved polysulfides. These characteristics of GOMC contribute to the improved rate capability and cyclability of the corresponding Li-S battery.