We study the quantum Hall effect (QHE) in graphene based on the current injection model, which takes into account the finite rectangular geometry with source and drain electrodes. In our model, the presence of disorder, the edge-state picture, extended states, and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.