The bursts of 40HzEEG are a reliable indicator of the " focused arousal ". It hasan active significance in diagnosis of cognitive dysfunction.But, the bursts of 40 Hz EEG are seriously interfered by the high amplitude broad-band EMG signals from the scalp. It causes the difficulty of detection, This paper give a new method uf the combination of threshold extraction in frequency domain and neural network pattern recognition to realize the effective detection of 40 Hz EEGbursts , and reports the mean peak power of the 40 HZ EEG bursts for 11 subjects and analyses theirthinking states, The reaults indicate that the method given in this paper can be used feasibly and support the theory given by D,E, Sheer.