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Cable incipient fault (CIF) is a potential fault which may recur over time and evolve into permanent fault eventually. The identification of CIF can help to reduce the likelihood of a permanent fault and enhance power supply reliability. This paper fully considers the randomness and uncertainty of CIF waveforms, and proposes a CIF identification method using power disturbance waveform feature learning. Firstly, the shallow features are extracted to characterize the transient components of different disturbance current waveforms, by conducting a stationary wavelet transform. Then, a dropout deep belief network (DDBN) is constructed using the extracted shallow features by pre-training and fine-tuning. Finally, the well- constructed DDBN model is used to identify CIF from other similar disturbance events. The performance of the proposed method is verified by simulation data and experimental data, for different disturbance events, such as sub-cycle cable incipient fault and multi-cycle cable incipient fault, as well as other over-current disturbance events such as capacitor switching and inrush current. Both the accuracy and generalization ability are higher than other methods. The proposed method provides new insights on possible applications on monitoring of cable status and timely warning of cable faults.