Carbon nanotube transistors, so far reported, had major problems such as a large time fluctuation of drain current and a large hysteresis characteristic. A cause of these fluctuations was found to be a photo-resist adhered to the surface of carbon nanotubes, as well as oxygen and water. New fabrication process for a carbon nanotube transistor was established in which the residue of the photo-resist as well as the water and oxygen never adhere to the carbon nanotubes. The new carbon nanotube transistor shows almost no fluctuation of the current and no hysteresis characteristic.