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A model is constructed to describe the electron emission from a vertically aligned monolayer graphene with a biased dc field. The graphene is excited by having an internal time-oscillating electric field. Our model has included all electrons from the central and sidebands. Due to the excitation, our calculations show that the electron emission is mostly due to the over-barrier electrons emission process, which is not sensitive to the surface potential barrier at the edge. By using a very small varying field of a few meV, a fairly large current line density in the order of nA/nm can be obtained. This paper should be useful for the development of laser-excited graphene-based photocathode.