Photogalvanic effect has been demonstrated to induce pure spin current in several spin polarized systems, but limited to specific photon energy or specific polarization/helicity angles of the incident light in any of the reported systems. The requirement of such a precise tuning to the specific photon energy or polarization/helicity angles makes it extremely difficult to achieve pure spin current practically. In this work, we propose a realization scheme with zigzag-edged graphene nanoribbons (ZGNRs) by edge passivation control. In detail, we divide a ZGNR into two halves, with one half monohydrogenated at the upper edge and dihydrogenerated at the lower edge, while the other half hydrogenated oppositely. By extensive first principles calculations, we show that pure spin current can always be generated, neither dependent of the photon energy and polarization/helicit angle, nor dependent of whether it is linearly, circularly or elliptically polarized. Such a robustness in pure spin current generation is found to originate from the inversion symmetry in the geometry structure and the spin semiconducting feature of the ZGNRs. This suggests a fantastic scheme for practically generating pure spin current with photogalvanic effect in graphene and will be of great significance in spintronics.