A random telegraph signal appears at a smaller absolute gate bias for a larger absolute drain-source bias in a carbon nanotube transistor. Its mechanism is attributed to a defect located in the drain side of the Schottky barrier carbon nanotube transistor with Ti∕Au as contact material. Furthermore, room temperature random telegraph signal is presented for both semiconducting and metallic carbon nanotubes, indicating the need to include random telegraph signal as a noise source for carbon nanotube transistors.