Bottom-up synthesized graphene nanoribbons and graphene nanoribbon heterostructures have promising electronic properties for high-performance field-effect transistors and ultra-low power devices such as tunneling field-effect transistors. However, the short length and wide band gap of these graphene nanoribbons have prevented the fabrication of devices with the desired performance and switching behavior. Here, by fabricating short channel (L _ch ~ 20 nm) devices with a thin, high-κ gate dielectric and a 9-atom wide (0.95 nm) armchair graphene nanoribbon as the channel material, we demonstrate field-effect transistors with high on-current (I _on > 1 μA at V _d = -1 V) and high I _on /I _off ~ 10⁵ at room temperature. We find that the performance of these devices is limited by tunneling through the Schottky barrier at the contacts and we observe an increase in the transparency of the barrier by increasing the gate field near the contacts. Our results thus demonstrate successful fabrication of high-performance short-channel field-effect transistors with bottom-up synthesized armchair graphene nanoribbons.