It is an important means to study the electrical activity of the brain's nerve cells by exploring physiological information of the EEGs from the frequency domain. The gravity frequency is one of the global parameters with using this method. We used the multitaper spectrum method (MTM) spectrum estimation method of good performance to calculate the EEG spectrum and its gravity frequency of subjects under vigilance and vigilance decrement state. The results showed that the gravity frequency of vigilance state was higher than that of vigilance decrement state, the gravity frequency became smaller along with the vigilance decrement, and the location of the gravity frequency shifted to the left in the spectrum. Finally, the monitoring curve of the gravity frequency was acquired by designing an algorithm, and it was used to online monitoring vigilance operators.