Drain current in an armchair graphene nanoribbon field effect transistor (AGNRFET) has been quantum mechanically modeled. The transfer matrix method (TMM) was employed to obtain the electron transmittance, and the obtained transmittance was then utilized to calculate the drain current by using the Landauer formula. The calculated results showed that the drain current increases with the gate and drain voltages. It was also shown that the threshold voltage for the device is around 0.3 V. In addition, the AGNR width influences the drain current of AGNRFET.