Sleep apnea syndrome (SAS) is a kind of harmful systemic sleep disorder with high incidence, and the pathological mechanism of it is complicated and the diagnosis and treatment are difficult. Mining the characteristic information of SAS from the single or small physiological signal is a hot topic in the research of sleep disorders in recent years. In our study shown in this paper, the detrended fluctuation analysis (DFA) was used to analyze sleep electroencephalogram (EEG) of SAS patients and normal healthy persons based on the non-stationary and nonlinear characteristics. It was found that in both groups, the scaling exponents increased gradually with the deepening of sleep, and in the rapid eye movement (REM) stage, the scaling exponents decreased. The scaling exponents of SAS group were significantly higher than those of the healthy group. The performance of SAS diagnosis based on scaling exponents was evaluated with receiver operator characteristic (ROC) curve. The optimal threshold value 0.81 for the SAS and normal control were obtained, corresponding to the sensitivity 94.4%, specificity 99.2%, and area under curve (AUC) was 0.994. The results show that DFA scaling exponents have a good discrimination power and accuracy for the SAS, which provide a new theoretical basis for SAS diagnosis.