The quality of sleep has a great relationship with health and working efficiency. The result of sleep stage classification is an important indicator to measure the quality of sleep, and it is also an important way to diagnose and treat sleep disorders. In this paper, the method of detrended cross-correlation analysis (DCCA) was used to analyze sleep stage classification, sleep electroencephalograph signals, which were extracted from the MIT-BIH Polysomnographic Database randomly. The results showed that the average DCCA exponent of the awake period is smaller than that of the first stage of non-rapid eye movement (NREM) sleeps. It is well concluded that the method of studying the sleep electroencephalograph with this method is of great significance to improve the quality of sleep, to diagnose and to treat sleep disorders.