At B3LYP level of theory, we predict that the half-metallicity in zigzag edge graphene nanoribbon (ZGNR) can be realized when an external electric field is applied across the ribbon. The critical electric field to induce the half-metallicity decreases with the increase of the ribbon width. Both the spin polarization and half-metallicity are removed when the edge state electrons fully transferred from one side to the other under very strong electric field. The electric field range under which ZGNR remain half-metallic increases with the ribbon width. Our study demonstrates a rich field-induced spin polarization behavior, which may leads to some important applications in spinstronics.