Sleep apnea is a kind of sleep disorder with a high prevalence rate. It is manifested as the abnormal stop of breathing during sleep and is highly dangerous to human health. The purpose of this research is to find a simple, and effective feature extraction method that can able to distinguish obstructive apnea events, central apnea events, and normal breathing events. Unlike conventional methods, the method illustrated in this study used the Infinite Impulse Response Butterworth Band pass filter to divide the Electroencephalogram (EEG) signal into 5, 7, 9 or 11 frequency sub-bands and then used the Welch method to extract the power features of these frequency sub-band signals, which were subsequently used as classifier input. Random forest, K-nearest neighbors and bagging classifiers were investigated. The results showed that in several different frequency sub-band division methods of EEG signals, the features extracted from the EEG signal that was divided into 11 frequency sub-bands were more conducive to the classification of sleep apnea events. The random forest classifier achieved the highest average accuracy, macro F1 and kappa coefficient in three types of events, which were 90.43%, 90.38% and 0.88, respectively. Compared with existing methods, the method used in the present study has higher classification performance.