We numerically investigate the valley-polarized current in symmetric and asymmetric zigzag graphene nanoribbons（ZGNRs） by the adiabatic pump, and the effect of spatial symmetry is considered by introducing different pumping regions. It is found that pumping potentials with the symmetry Vp（x,y） = Vp（-x,y）can generate the largest valleypolarized current. The valley-polarized currents I13L with the pumping potential symmetry Vp（x,y） =Vp（x,-y,） and I14L with Vp（x,y） = Vp（-x,-y） of symmetric ZGNRs are much smaller than those of asymmetric ZGNRs. We also find I13L and I14L 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.
