Topological defects are widely recognized as effective active sites toward a variety of electrochemical reactions. However, the role of defect curvature is still not fully understood. Herein, carbon nanomaterials with rich topological defect sites of tunable curvature is reported. The curved defective surface is realized by controlling the high-temperature pyrolytic shrinkage process of precursors. Theoretical calculations demonstrate bending the defect sites can change the local electronic structure, promote the charge transfer to key intermediates, and lower the energy barrier for oxygen reduction reaction (ORR). Experimental results convince structural superiority of highly-curved defective sites, with a high kinetic current density of 22.5 mA cm−2 at 0.8 V versus RHE for high-curvature defective carbon (HCDC), ≈18 times that of low-curvature defective carbon (LCDC). Further raising the defect densities in HCDC leads to the dual-regulated products (HCHDC), which exhibit exceptionally outstanding ORR activity in both alkaline and acidic media (half-wave potentials: 0.88 and 0.74 V), outperforming most of the reported metal-free carbon catalysts. This work uncovers the curvature-activity relationship in carbon defect for ORR and provides new guidance to design advanced catalysts via curvature-engineering.