Sleep apnea is a kind of widespread and serious sleep disorder that disrupts breathing during the sleep of apnea patients. Clinically, sleep apnea events can be monitored and manually scored from whole-night polysomnography by specialists. However, this task tends to be time-consuming and error-prone. In this paper, we propose an automatic sleep apnea detection scheme using single-channel electroencephalography (EEG)signals. The segmented EEG signals with a length of 30-second are firstly filtered by a band-pass filter to denoise. A short time Fourier transform is then used to generate the time-frequency images from corresponding EEG signals. A multi-scale parallel convolutional neural network with mixed depth of layers and mixed sizes of convolutional filters is designed to automatically learn the features from time-frequency representations and make the classification between sleep apnea periods and other periods. Experimental results show the superior performance of the proposed method in terms of sensitivity, specificity, and accuracy, compared to state-of-the-art works. This method provides the possibility to record and analyze the sleep apnea automatically in sleep monitoring.