An analog of the Datta-Das spin field-effect transistor (FET) is investigated, which is all graphene and based on the valley degree of freedom of electrons/holes. The "valley FET" envisioned consists of a quantum wire of gapped graphene (channel) sandwiched between two armchair graphene nanoribbons (source and drain), with the following correspondence to the spin FET: valley (K and K') <-> spin (up and down), armchair graphene nanoribbons <-> ferromagnetic leads, graphene quantum wire <-> semiconductor quantum wire, valley-orbit interaction <-> Rashba spin-orbit interaction. The device works as follows. The source (drain) injects (detects) carriers in a specific valley polarization. A side gate electric field is applied to the channel and modulates the valley polarization of carriers due to the valley-orbit interaction, thus controlling the amount of current collected at the drain. The valley FET is characterized by (i) smooth interfaces between leads and the channel, (ii) strong valley-orbit interaction for electrical control of drain current, and (iii) vanishing interband valley-flip scattering. By its analogy to the spin FET, the valley FET provides a potential framework to develop low-power FETs for graphene-based nanoelectronics.