Using a polymer-masking approach, we have developed metal-free 2D carbon electrocatalysts based on single-layer graphene with and without punched holes and/or N-doping. A combined experimental and theoretical study on the resultant 2D graphene electrodes revealed that a single-layer graphene sheet exhibited a significantly higher electrocatalytic activity at its edge than that over the surface of its basal plane. Furthermore, the electrocatalytic activity of a single-layer 2D graphene sheet was significantly enhanced by simply punching microholes through the graphene electrode due to the increased edge population for the hole-punched graphene electrode. In a good consistency with the experimental observations, our density function theory calculations confirmed that the introduction of holes into a graphene sheet generated additional positive charge along the edge of the punched holes and hence the creation of more highly active sites for the oxygen reduction reaction. The demonstrated concept for less graphene material to be more electrocatalytically active shed light on the rational design of low-cost, but efficient electrocatalysts from 2D graphene for various potential applications ranging from electrochemical sensing to energy conversion and storage.