In this work we calculate the I-V characteristics of Fe/MgO/Fe(100) tunneling junctions from first principles. First we investigate the zero-bias transmission coefficients T(E) as a function of the energy for either collinear parallel or antiparallel configurations of the magnetic leads. The zero bias calculations are then compared to the self-consistent calculations at finite bias. For small bias voltage there is a significant contribution from the minority spin channel to the current in the parallel configuration, which is due to resonant surface states. As a bias of about 25 mV is applied the surface states get out of resonance and the current through the minority spin channel saturates, so that the main current flows through the majority spin.