Sleep is important for the restoration and renewal of the human body. Obstructive sleep apnea syndrome (OSAS), which is caused by repetitive episodes of partial or complete upper airway obstruction during sleep, is the most common type of sleep apnea. The sleep electroencephalogram (EEG) analysis has been an important tool to investigate brain activity. In this study, we used the spectral analysis and fuzzy entropy to analyze the EEG signals collected from the OSAS patients and normal control. Results obtained from the EEG power spectrum and fuzzy entropy with and without principal component analysis (PCA) process were used as the features and fed into four different classifiers, namely, linear Support Vector Machines (SVM), Liner Discriminant Analysis (LDA), subspace k-nearest neighbor (k-NN) and subspace discriminant analysis, to differentiate these two groups. Our results demonstrated that the feature resulted from power spectrum with PCA process and subspace discriminate method using 5-fold cross-validation produces the superior classification rate which is 89 ± 3.74%.