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 multi-label K-nearest neighbor (ML-KNN) algorithm is one of them. However, as a first-order algorithm, ML-KNN ignores the relationship between labels. In this study, a hierarchical multi-label learning algorithm is proposed, named hierachical multi-label K-nearest neighbor (HML-KNN). 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. HML-KNN algorithm is a high-order algorithm, which considers the global label information. Through the verification on XJTU-SY bearing data set, the superiority of HML-KNN algorithm in dealing with composite fault diagnosis is demonstrated.