Graphene has the advantages of high electrical conductivity, high heat conductivity, and low noise, which makes it a potential option for integrated circuits interconnection and nanoelectrodes. In this paper, we present a novel fabrication method for graphene nanoeletrodes with nanogap. First, graphene grown by chemical vapor deposition (CVD) is assembled to a chip with microelectrodes. Second, an atomic force microscopy (AFM) based mechanical cutting method is developed to cut the graphene into nanoribbons and nanoeletrodes with nanogap. Then the electronic property of a single nanodot is characterized using the garphene nanoelectrodes, demonstrating the effectiveness of the graphene nanoelectrodes. The fabricated graphene nanoeletrode pairs can be used as probes to detect single molecule in micro-environment, and show an attractive prospect for future molecular electronics applications.