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The detection of broken wires in steel wire ropes is of great significance for the production safety. However, the existing identification techniques mainly focus on the external broken wires problem. Here, the artificial feature extraction is one of the most important method, while only the prior knowledge of the artificial feature extraction method is adequate, the identification precision can be satisfied. Therefore, it is still a challenge to realize intelligent diagnosis for the broken wires. Besides, the identification of internal broken wires problem is still not well solved. In this paper, a quantitative identification method based on continuous wavelet transform (CWT) and convolutional neural network (CNN) is proposed to solve the internal and external broken wires identification problem. The key technology of this research is that the fault information from the time-frequency images converted by the magnetic flux leakage (MFL) signals can be automatically extracted through a designed CNN. The main innovation is that the complex signal processing work can be eliminated and the internal and external broken wires can be accurately identified simultaneously by combining CWT and CNN. The experimental results of a steel wire rope test rig are compared with the traditional recognition method, which shows that the proposed method achieved significant improvement on detection accuracy and recognition performance.