By carrying out density functional theory analysis within the Keldysh non-equilibrium Green's functional formalism, we have calculated the nonlinear and non-equilibrium quantum transport properties of Fe/MgO/Fe trilayer structures as a function of external bias voltage. For well relaxed atomic structures of the trilayer, the equilibrium tunnel magnetoresistance ratio (TMR) is found to be very large and also fairly stable against small variations in the atomic structure. As a function of external bias voltage, the TMR reduces monotonically to zero with a voltage scale of about 1V, in agreement with experimental observations. We present understanding of the nonequilibrium transport properties by investigating microscopic details of the scattering states and the Bloch bands of the Fe leads.PACS numbers: 85.35.-p, 72.25.-b, 85.65.+h Since the prediction and elegant physics explanation [1,2] that magnetic tunnel junction (MTJ) of Fe/MgO/Fe trilayer structure may have very high tunnel magnetoresistance (TMR), MgO based MTJ has progressed at a rapid pace in recent years and produced the highest measured TMR at room temperature: several groups [3,4] reported TMR ratio in the range of 180% to 250%. TMR effect presents an excellent opportunity for spintronics, it is the key to magnetoresistive random-access-memory . There are, however, a number of important issues remain to be understood from atomic first principles. Most existing work predicted[1, 2] TMR to be greater than 1000%, experimental data are still lower. More seriously is that experimental data on MgO based MTJs show a monotonically decreasing TMR as a function of applied bias voltage [3,4] and it reduces to zero when bias is about one volt. To the best of our knowledge, there have been two atomistic calculations of bias dependence of TMR for MgO barriers [7,8], both used the Korringa-Kohn-Rostoker numerical technique. Ref.7 predicted a substantial increase of TMR versus bias for the asymmetric system analyzed there, while Ref.8 found a roughly constant TMR, a decaying TMR, or an entirely negative TMR versus bias depending on atomic structures of the interface. The origin of these differences were not clear. Earlier theory[9] on Al 2 O 3 based MTJs has attributed small bias dependence of magneto-resistance to magnon scattering. Given the extreme importance of MgO based MTJ in near future spintronics and the accumulated experimental data, further quantitative understanding on quantum transport in Fe/MgO/Fe at finite bias is urgently needed.Here we present a first principles atomistic analysis of nonlinear and non-equilibrium quantum transport in Fe/MgO/Fe MTJ. We use a state-of-the-art quantum transport technique [10,11] which is based on real-space, Keldysh nonequilibrium Green's function (NEGF) formalism combined with density functional theory (DFT). The basic idea of the NEGF-DFT formalism [10] is to calculate device Hamiltonian and electronic structure by DFT, populate this electronic structure using NEGF which properly takes into account nonequilibrium q...