Manipulation of single electrons is the key to developing ultimate electronics such as single-electron-based information processors and electrical standards in metrology. Especially, high-frequency and high-accuracy single-electron pumps are essential to realize practical current standards. While electrically defined quantum dots are widely used to build single-electron pumps, a localized state in semiconductors is also a potential candidate for accurate pumps because it can have a large activation energy for the captured electron. However, the transfer mechanism of such localized-state-mediated single-electron pumps for high-accuracy operation at a high frequency has not been well examined. Here we demonstrate a single-electron pump using a single-trap level with an activation energy of a few ten millielectron volts in Si nanotransistors. By means of gate control of capture and emission rates, the pump operates at a frequency of 3 GHz with an accuracy of better than 10(-3) at 17 K, indicating that an electric field at the trap level lowers the capture and emission time to less than 25 ps.