A micro-sleep is a short sleep that lasts from 1 to 30 secs. Its detection during driving is crucial to prevent accidents that could claim a lot of people's lives. Electroencephalogram (EEG) is suitable to detect micro-sleep because EEG was associated with consciousness and sleep. Deep learning showed great performance in recognizing brain states, but sufficient data should be needed. However, collecting micro-sleep data during driving is inefficient and has a high risk of obtaining poor data quality due to noisy driving situations. Night-sleep data at home is easier to collect than micro-sleep data during driving. Therefore, we proposed a deep learning approach using night-sleep EEG to improve the performance of micro-sleep detection. We pre-trained the U-Net to classify the 5-class sleep stages using night-sleep EEG and used the sleep stages estimated by the U-Net to detect micro-sleep during driving. This improved micro-sleep detection performance by about 30\% compared to the traditional approach. Our approach was based on the hypothesis that micro-sleep corresponds to the early stage of non-rapid eye movement (NREM) sleep. We analyzed EEG distribution during night-sleep and micro-sleep and found that micro-sleep has a similar distribution to NREM sleep. Our results provide the possibility of similarity between micro-sleep and the early stage of NREM sleep and help prevent micro-sleep during driving.