It is necessary to identify the cable incipient faults in order to eliminate the hidden faults in time. This paper proposes a method for cable incipient fault classification and identification based on Convolution Neural Network (CNN). This method can identify the cable incipient fault from the over-current disturbance waveforms, including the waveforms of constant impedance fault, inrush current, capacitance switching disturbance waveform, and so on. The features of the over-current waveforms are extracted by wavelet transform, which are used as the input of CNN. By training the mapping relationship between input features and class coding, the parameter is chosen and the CNN is formed. CNN is optimized by modifying the loss function and adopting the method of adaptive learning rate, for solving the problem of over-fitting and learning efficiency. The simulation results show that the proposed method can classify the overcurrent signals effectively and identify cable incipient fault accurately, which is with high engineering application value. This work is supported by National Natural Science Foundation of China (No. 51807126).