We investigated the vacuum potential barriers of various graphene edges terminated with hydrogen, oxygen, hydroxyl group and ether group, respectively. It is found that the exchange-correlation potential correction is significant to the edge structures with electronegativity higher than carbon. The correction leads to the local work function decreased by more than 1 eV for the O terminated edge, while the local work function of H and OH terminated edges remain unchanged. (C) 2011 Published by Elsevier B. V.