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The spin dependent charge transport in zigzag graphene nanoribbons (ZGNRs) has been investigated by the nonequilibrium Green’s function method combined with the density functional theory at the local spin density approximation. The current versus voltage curve shows distinguished behaviors for symmetric and asymmetric ZGNRs, and the doping on the ZGNR edges can manipulate the spin transport. In special cases that a Be atom is substitutionally doped on one edge of the symmetric ZGNRs, one spin current shows negative differential resistance, whereas the other increases monotonically with the bias. This property might be used to design spin oscillators or other devices for spintronics.