Using the density-functional theory, the structural stability and the effect of in-plane electric field on the electronic structure of zigzag graphene nanoribbin (OH-ZGNR), which is terminated by hydroxyl, are explored. It is found that hydroxyl bonding on the ZGNR edge is much more stable than H-terminated ZGNR(H-ZGNRs). The ground state of the ZGNR is spin-polarized with a narrow energy gap. Furthermore, transition from semiconducting to metallic phase in ZGNR can be achieved if a proper in-plane electric field is applied across the edges OH-ZGNR.