In this paper, a deep learning (DL)-based method for automatic feature extraction and classification of voltage dips is proposed. The method consists of a dedicated architecture of Long Short-Term Memory (LSTM), which is a special type of Recurrent Neural Networks (RNNs). A total of 5982 three-phase one-cycle voltage dip RMS sequences, measured from several countries, has been used in our experiments. Our results have shown that the proposed method is able to classify the voltage dips from learned features in LSTM, with 93.40% classification accuracy on the test data set. The developed architecture is shown to be novel for feature learning and classification of voltage dips. Different from the conventional machine learning methods, the proposed method is able to learn dip features without requiring transition-event segmentation, selecting thresholds, and using expert rules or human expert knowledge, when a large amount of measurement data is available. This opens a new possibility of exploiting deep learning technology for power quality data analytics and classification.