Accurate identification of cable incipient fault is helpful to reduce the failure rate of power system and improve the reliability of power supply. In the traditional pattern recognition method, it is difficult to select the efficient features, which are beneficial to classification, therefore, it would affect the accuracy of recognition. In view of this, this paper applies the Deep Learning (DL) network stacked from multiple non-negative constraint autoencoders to recognize cable incipient fault. In order to improve the learning efficiency of DL network, firstly, stationary wavelet transform of the fault phase current is used to extract the primary characteristics with correlation and redundancy, e. g. some statistics, energy entropy and information entropy. And then DL network is constructed by stacking multiple nonnegative constraint autoencoders. After preliminary training and fine-tuning training process, some effective features for recognition are learned from primary features. Finally, Softmax classifier is used to identify the cable incipient fault from normal state and other disturbances. Experiments on cable current simulation data are done, and the results show that the method is more accurate than the traditional pattern recognition method. This work is supported by Science and Technology Project of State Grid Liaoning Electric Power Company (No. 5602/2018-28001B).