A non-linear element (e.g., a diode) with small reverse saturation current is provided. A non-linear element includes a first electrode provided over a substrate, an oxide semiconductor film provided on and in contact with the first electrode, a second electrode provided on and in contact with the oxide semiconductor film, a gate insulating film covering the first electrode, the oxide semiconductor film, and the second electrode, and a third electrode provided in contact with the gate insulating film and adjacent to a side surface of the oxide semiconductor film with the gate insulating film interposed therebetween or a third electrode provided in contact with the gate insulating film and surrounding the second electrode. The third electrode is connected to the first electrode or the second electrode.