Gearboxes are the most widely used elements for transferring speed and power in many industrial machines. High-precision gearbox fault diagnosis is quite significant for keeping the machine systems work normally and safe. Owing to various unseen single or compound faults, it is pretty difficult to realize high-precision intelligent fault diagnosis of gearboxes using existing methods. In addition, existing intelligent fault diagnosis solutions heavily rely on manual feature extraction and selection using complicated signal processing techniques. In this study, a novel compound fault diagnosis method of the gearbox is proposed by integrating convolutional neural network (CNN) with wavelet transform (WT) and multi-label (ML) classification, namely WT-MLCNN. The developed WT-MLCNN approach involves two parts. In the first part, WT is adopted to extract 2-D time-frequency features from raw 1-D vibration signals. In the second part, the extracted features are inputted into the built MLCNN model to realize compound fault diagnosis of the gearbox. Two main contributions are concluded by comparing to the previous works: first, the proposed method directly uses raw vibration signals to carry out fault diagnosis in an end-to-end way, greatly reducing the reliance on human expertise and manual intervention; second, the appropriate network architecture of the MLCNN model is designed to realize compound fault diagnosis of the gearbox effectively and efficiently. Finally, two case studies are implemented to verify the presented method. The results indicate that it can achieve higher accuracy than other existing methods in literatures. Moreover, its performance in stability is pretty good as well