Using the density functional theory and the nonequilibrium Green's function method, we studied the finite-bias quan- tum transport in a Cr/graphene/Cr magnetotunnel junction (MTJ) constructed by a single graphene layer sandwiched be- tween two semi-infinite Cr(111 ) electrodes. We found that the tunneling magnetoresistance (TMR) ratio in this MTJ reached 108%, which is close to that of a perfect spin filter. Under an external positive bias, we found that the TMR ratio remained constant at 65%, in contrast to MgO-based MTJs, the TMR ratios of which decrease with increasing bias. These results indicate that the Cr/graphene/Cr MTJ is a promising candidate for spintronics applications.