The rational design of a stable and catalytic carbon cathode is crucial for the development of rechargeable lithium-oxygen (LiO2 ) batteries. An edge-site-free and topological-defect-rich graphene-based material is proposed as a pure carbon cathode that drastically improves LiO2 battery performance, even in the absence of extra catalysts and mediators. The proposed graphene-based material is synthesized using the advanced template technique coupled with high-temperature annealing at 1800°C. The material possesses an edge-site-free framework and mesoporosity, which is crucial to achieve excellent electrochemical stability and an ultra-large capacity (>6700 mAh g-1 ). Moreover, both experimental and theoretical structural characterization demonstrates the presence of a significant number of topological defects, which are non-hexagonal carbon rings in the graphene framework. In situ isotopic electrochemical mass spectrometry and theoretical calculations reveal the unique catalysis of topological defects in the formation of amorphous Li2 O2 , which may be decomposed at low potential (∼ 3.6V versus Li/Li+ ) and leads to improved cycle performance. Furthermore, a flexible electrode sheet that excludes organic binders exhibits an extremely long lifetime of up to 307 cycles (>1535h), in the absence of solid or soluble catalysts. These findings may be used to design robust carbon cathodes for LiO2 batteries.