Incipient faults in power cables are a serious threat to power safety and are difficult to accurately identify. The traditional pattern recognition method based on feature extraction and feature selection has strong subjectivity. If the key feature information cannot be extracted accurately, the recognition accuracy will directly decrease. To accurately identify incipient faults in power cables, this paper combines a sparse autoencoder and a deep belief network to form a deep neural network, which relies on the powerful learning ability of the neural network to classify and identify various cable fault signals, without requiring preprocessing operations for the fault signals. The experimental results demonstrate that the proposed approach can effectively identify cable incipient faults from other disturbances with a similar overcurrent phenomenon and has a higher recognition accuracy and reliability than the traditional pattern recognition method.