Graphene has unique electronic properties1,2 and graphene nanoribbons are of particular interest because they exhibit a conduction band gap, which arises due to size confinement and edge effects3-11. Theoretical studies have suggested that graphene nanoribbons could have interesting magneto-electronic properties with very large magnetoresistance predicted4,12-20. Here we report the experimental observation of a significant enhancement in the conductance of a graphene nanoribbon field-effect transistor in a perpendicular magnetic field. A negative magnetoresistance of nearly 100% was observed at low temperatures, with over 50% remaining at room temperature. This magnetoresistance can be tuned by varying the gate or source-drain bias. We also find that the charge transport in the nanoribbons is not significantly modified by an in-plane magnetic field. The large values of the magnetoresistance we observe may be attributed to the reduction of quantum confinement by the formation of cyclotron orbits and the delocalization effect under the perpendicular magnetic field15-20.