Traditional fault diagnosis methods are mostly for a single fault type at one time, but in the actual industry, many kinds of faults will occur at the same time, that is compound fault. For the problem of compound fault diagnosis, some scholars have introduced the method of multi-label learning, and the multi-label K-nearest neighbor (ML-KNN) algorithm is one of them. However, as a first-order algorithm, the ML-KNN algorithm only considers the relationship between the label and the corresponding sample data, but ignores the relationship between the labels. In this study, a hierarchical multi-label learning algorithm is proposed, named hierachical multi-label K-nearest neighbor (HML-KNN). The HML-KNN algorithm categorizes the degradation state as the first level and fault type of machinery as the second level. The first level label information is transformed, and the transformed information is put into the second level as new features for judgment. The HML-KNN algorithm is a high-level algorithm that takes into account the global label information, and includes the feature conversion of the label, which makes the result more accurate. Through the verification on the XJTU-SY bearing data set, the superiority of the HML-KNN algorithm in dealing with compound fault diagnosis is demonstrated.