An analogue of the Datta-Das spin 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') \leftrightarrow spin (up and down), armchair graphene nanoribbons \leftrightarrow ferromagnetic electrodes, graphene quantum wire \leftrightarrow semiconductor quantum wire, valley-orbit interaction \leftrightarrow Rashba spin-orbit interaction. The device works as follows. The source (drain) injects (detects) carriers in a specific valley polarization. A 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 electrodes 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.