Surface oxidized carbon nanotubes (o-CNTs) can produce sustainable hydrogen peroxide (H2O2) by the two-electron transferred oxygen reduction reaction (2e-ORR). The C atoms neighboring to surface epoxy (C-O-C) groups are recognized as active sites. Herein, we report the CNT curvature, or diameter, dependent ORR activity of o-CNT catalysts. Computation modeling suggests that the curvature can alter epoxy group geometry, exerting greater strain on the C-O bond in smaller diameter o-CNTs that leads to improved activity. This theoretical prediction is further experimentally validated by five o-CNTs of different diameters but comparable oxygenous groups. The o-CNT with the smallest diameter (8 nm) delivers the highest H2O2 Faradaic efficiency (>85%, or molar selectivity >90%) and a mass activity of 161 A g-1 at 0.65 V. This curvature effect provides a strategy to design and synthesize efficient electrocatalysts for peroxide production and beyond.