The gate dependence of a Coulomb attractive random telegraph signal is observed in a single-walled carbon nanotube field effect transistor for temperatures varying from 0.32 to 24 K. The mechanism of the Coulomb attractive random telegraph signal is attributed to the carrier tunneling between the carbon nanotube and the Coulomb attractive defect. The random telegraph signal is also studied under magnetic field over an entire gate bias range and a wide temperature range. The Coulomb attractive random telegraph signal shows weak magnetic dependence, which may be due to the broadening of the Zeeman levels of the defect in the p-type carbon nanotube field effect transistor.