The electroencephalogram (EEG) is the most prominent means to study epilepsy and capture changes in electrical brain activity that could declare an imminent seizure. In this work, Long Short-Term Memory (LSTM) networks are introduced in epileptic seizure prediction using EEG signals, expanding the use of deep learning algorithms with convolutional neural networks (CNN). A pre-analysis is initially performed to find the optimal architecture of the LSTM network by testing several modules and layers of memory units. Based on these results, a two-layer LSTM network is selected to evaluate seizure prediction performance using four different lengths of preictal windows, ranging from 15 min to 2 h. The LSTM model exploits a wide range of features extracted prior to classification, including time and frequency domain features, between EEG channels cross-correlation and graph theoretic features. The evaluation is performed using long-term EEG recordings from the open CHB-MIT Scalp EEG database, suggest that the proposed methodology is able to predict all 185 seizures, providing high rates of seizure prediction sensitivity and low false prediction rates (FPR) of 0.11-0.02 false alarms per hour, depending on the duration of the preictal window. The proposed LSTM-based methodology delivers a significant increase in seizure prediction performance compared to both traditional machine learning techniques and convolutional neural networks that have been previously evaluated in the literature.