A method for manufacturing a field-effect transistor is provided. The field-effect transistor includes on a substrate a source electrode, a drain electrode, an oxide semiconductor layer, an insulating layer and a gate electrode. The method includes, after forming the insulating layer on the oxide semiconductor layer, an annealing step of increasing the electrical conductivity of the oxide semiconductor layers by annealing in an atmosphere containing moisture. The steam pressure at the annealing step is higher than the saturated vapor pressure in the atmosphere at the annealing temperature.