Seizures during sleep increase the probability of complication and sudden death. Effective prediction of seizures in sleep allows doctors and patients to take timely treatments to reduce the aforementioned probability. Most of the existing methods make use of electroencephalogram (EEG) to predict seizures, which are not specific developed for the sleep. However, EEG during sleep has its characteristics compared with EEG during other states. Therefore, in order to improve the sensitivity and reduce the false alarm rate, this paper utilized the characteristics of EEG to predict seizures during sleep. We firstly constructed the feature vector including the absolute power spectrum, the relative power spectrum and the power spectrum ratio in different frequencies. Secondly, the separation criterion and branch-and-bound method were applied to select features. Finally, support vector machine classifier were trained, which is then employed for online prediction. Compared with the existing method that do not consider the characteristics of sleeping EEG (sensitivity 91.67%, false alarm rate 9.19%), the proposed method was superior in terms of sensitivity (100%) and false alarm rate (2.11%). This method can improve the existing epilepsy prediction methods and has important clinical value.