For patients with Type 1 Diabetes Mellitus (T1DM), hypoglycemia is a very common but dangerous complication which can lead to unconsciousness, coma and even death. The variety of hypoglycemia symptoms is originated from the inadequate supply of glucose to the brain. In this study, we explore the connection between hypoglycemic episodes and the electrical activity of neurons within the brain or electroencephalogram (EEG) signals. By analyzing EEG signals from a clinical study of five children with T1DM, associated with hypoglycemia at night, we find that some EEG parameters change significantly under hypoglycemia condition. Based on these parameters, a method of detecting hypoglycemic episodes using EEG signals with a feed-forward multi-layer neural network is proposed. In our application, the classification results are 72% sensitivity and 55% specificity when the EEG signals are acquired from 2 electrodes C3 and O2. Furthermore, signals from different channels are also analyzed to observe the contributions of each channel to the performance of hypoglycemia classification.