Layered lithium cobalt oxide (LiCoO2, LCO) is the most successful commercial cathode material in lithium-ion batteries. However, its notable structural instability at potentials higher than 4.35 V (versus Li/Li+) constitutes the major barrier to accessing its theoretical capacity of 274 mAh g-1. Although a few high-voltage LCO (H-LCO) materials have been discovered and commercialized, the structural origin of their stability has remained difficult to identify. Here, using a three-dimensional continuous rotation electron diffraction method assisted by auxiliary high-resolution transmission electron microscopy, we investigate the structural differences at the atomistic level between two commercial LCO materials: a normal LCO (N-LCO) and a H-LCO. These powerful tools reveal that the curvature of the cobalt oxide layers occurring near the surface dictates the structural stability of the material at high potentials and, in turn, the electrochemical performances. Backed up by theoretical calculations, this atomistic understanding of the structure-performance relationship for layered LCO materials provides useful guidelines for future design of new cathode materials with superior structural stability at high voltages.