A method is proposed to calculate and analyze electro-encephalogram signal to improve the situation that there is an urgent need for an effective quantitative indicator to describe brain mental disorders. The method defines a spectral entropy in terms of the power spectrum division of time series. Then, the entropy is applied to numerical calculation of electroencephalogram signals of depression patients and normal control group. Meanwhile, the differences are compared between them. Experimental results show that the power spectral entropy in depression patients is significantly weaker than the normal healthy people's in some brain regions. Further analysis proves two facts. One is that the entropy is positively correlated to brain electrical physiological activity, and the other tells that the entropy can be used as a parameter to measure brain electrical activity, to characterize brain electrical physiological activities, and to provide the activity intensity information. This paper determines that the power spectral entropy for electroencephalogram plays an important role in diagnosis of brain mental disorder.