To classify between normal and sleep apnea subjects based on sub-band decomposition of electroencephalogram (EEG) signals. This study comprised 159 subjects obtained from the ISRUC (Institute of System and Robotics—University of Coimbra), Sleep-EDF (European Data Format), and CAP (Cyclic Alternating Pattern) Sleep database, which consists of normal and sleep apnea subjects. The wavelet packet decomposition method was incorporated to categorize the EEG signals into five frequency bands, namely, alpha, beta, delta, gamma, and theta. Entropy and energy (non-linear) for all bands was calculated and as a result, 10 features were obtained for each EEG signal. The ratio of EEG bands included four parameters, including heart rate, brain perfusion, neural activity, and synchronization. In this study, a support vector machine with kernels and random forest classifiers was used for classification. The performance measures demonstrated that the improved results were obtained from the support vector machine classifier with a kernel polynomial order 2. The accuracy (90%), sensitivity (100%), and specificity (83%) with 14 features were estimated using the data obtained from ISRUC database. The proposed study is feasible and seems to be accurate in classifying the subjects with sleep apnea based on the extracted features from EEG signals using a support vector machine classifier.