Electrical current can be completely spin polarized in a class of materials known as half-metals, as a result of the coexistence of metallic nature for electrons with one spin orientation and insulating nature for electrons with the other. Such asymmetric electronic states for the different spins have been predicted for some ferromagnetic metals--for example, the Heusler compounds--and were first observed in a manganese perovskite. In view of the potential for use of this property in realizing spin-based electronics, substantial efforts have been made to search for half-metallic materials. However, organic materials have hardly been investigated in this context even though carbon-based nanostructures hold significant promise for future electronic devices. Here we predict half-metallicity in nanometre-scale graphene ribbons by using first-principles calculations. We show that this phenomenon is realizable if in-plane homogeneous electric fields are applied across the zigzag-shaped edges of the graphene nanoribbons, and that their magnetic properties can be controlled by the external electric fields. The results are not only of scientific interest in the interplay between electric fields and electronic spin degree of freedom in solids but may also open a new path to explore spintronics at the nanometre scale, based on graphene.