We numerically investigate the valley-polarized current in symmetric and asymmetric zigzag graphene nanorib-bons (ZGNRs) by the adiabatic pump, and the effect of spatial symmetry is considered by introducing different pump-ing regions. It is found that pumping potentials with the symmetry Vp(x,y)=Vp(?x,y) can generate the largest valley-polarized current. The valley-polarized currents IL13 with the pumping potential symmetry Vp(x,y)=Vp(x,?y) and IL14 with Vp(x,y)=Vp(?x,?y) of symmetric ZGNRs are much smaller than those of asymmetric ZGNRs. We also find IL13 and IL14 of symmetric ZGNRs decrease and increase with the increasing pumping amplitude, respectively. Moreover, the dephasing effect from the electron–phonon coupling within the Buttiker dephasing scheme is introduced. The valley-polarized current of the symmetric ZGNRs with Vp(x,y)=Vp(x,?y) increases with the increase of the dephasing strength while that with Vp(x,y)=Vp(?x,?y) decreases as the dephasing strength increases.