In a rectifier circuit, by using a transistor whose off-state current is small as a so-called diode-connected MOS transistor included in the rectifier circuit, breakdown which is caused when a reverse bias is applied is prevented. Thus, an object is to provide a rectifier circuit whose reliability is increased and rectification efficiency is improved. A gate and a drain of a transistor are both connected to a terminal of the rectifier circuit to which an AC signal is input. In the transistor, an oxide semiconductor is used for a channel formation region and the off-state current at room temperature is less than or equal to 10−20 A/μm, which is equal to 10 zA/μm (z: zepto), when the source-drain voltage is 3.1 V.