This paper presents an investigation of the nonlinear problem of electrically actuated single-walled carbon nanotube. A clamped-clamped carbon nanotube connected to the fixed electrode plate,forming a capacitor under the external excitation voltage. According to the beam theory,the nonlinear dynamic equation of carbon nanotube system is established,it is a nonlinear partial differential equation. By means of the method of multiple scales,nonlinear vibration equation of the system is acquired and the numerical calculation is carried out. Numerical analysis of the influence of different parameters is analyzed.With the increase of carbon nanotube length and AC voltage,the amplitude and the unstable interval become larger. With the increase of carbon nanotube radius and plate distance,the amplitude and the unstable interval become smaller. Whenσis close to zero,the amplitude of the response curves hardly changes with the other system parameters.