Graphene has unique electronic properties, and graphene nanoribbons are of particular interest because they exhibit a conduction bandgap that arises due to size confinement and edge effects. Theoretical studies have suggested that graphene nanoribbons could have interesting magneto-electronic properties, with a very large predicted magnetoresistance. Here, we report the experimental observation of a significant enhancement in the conductance of a graphene nanoribbon field-effect transistor by a perpendicular magnetic field. A negative magnetoresistance of nearly 100% was observed at low temperatures, with over 50% magnetoresistance 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 observed values of magnetoresistance may be attributed to the reduction of quantum confinement through the formation of cyclotron orbits and the delocalization effect under the perpendicular magnetic field.