Abstract: We present a theoretical investigation on the transport properties of graphene in the presence of high dc driving fields. Considering electron interactions with impurities and acoustic and optical phonons in graphene, we employ the momentum- and energy-balance equations derived from the Boltzmann equation to self-consistently evaluate the drift velocity and temperature of electrons in graphene in the linear and nonlinear response regimes. We find that the current-voltage relation exhibits distinctly nonlinear behavior, especially in the high electric field regime. Under the action of high-fields the large source-drain (sd) current density can be achieved and the current saturation in graphene is incomplete with increasing the sd voltage Vsd up to 3 V. Moreover, for high fields, Vsd>0.1 V, the heating of electrons in graphene occurs. It is shown that the sd current and electron temperature are sensitive to electron density and lattice temperature in the graphene device. This study is relevant to the application of graphene as high-field nano-electronic devices such as graphene field-effect transistors.