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Magnetic flux leakage (MFL) testing, non-destructive testing, can prevent some major accidents of hoist equipment by identifying the damage of wire ropes. However, in harsh working conditions such as mines and oil wells, the inevitable vibration and swing of wire rope will generate noise and interfere with the MFL signal, which makes us difficult to identify the damage. As a classification network, Convolutional neural network (CNN) is positive in recognition accuracy and noise resistance, but it hardly uses in wire rope damage classification. To improve the accuracy of wire rope damage identification under noise background, we propose a method of wire rope damage identification via Light-EfficientNetV2 and MFL image. First, the MFL signal is segmented and rearranged to form the MFL image, and then the image is classified by Light-EfficientNetV2. To improve the classification efficiency, we reduce the layers of EfficientNetV2 to make it lighter. Finally, the availability of this method is proved by the validation set. Compared with four neural networks, the accuracy is the highest. Moreover, as the noise increased, the accuracy of Light-EfficientNetV2 is higher than EfficientNetV2, which has application value in the wire rope damage identification under noise background.