The diagnosis of compound faults in complex hydraulic systems is a major difficulty. The number of labels will grow exponentially as the number of fault types increases and fault degrees vary. A diagnosis method based on principal component analysis (PCA) and multi-output support vector machine (SVM) is proposed for this problem. Firstly, by calculating Spearman ranking correlation coefficients of time domain features extracted from multiple sensor signals and each type of fault, the most relevant features are selected, and after dimensionality reduction with PCA, the dataset is constructed. The second is to design a multi-output classifier based on SVM and One-vs-all. Finally, the diagnosis model is evaluated with four indicators including accuracy, precision, recall rate and F1 score. The result indicates that the proposed method can effectively identify all the single faults, fault combinations and their severities at the same time. And the method performs better than diagnosing each type of fault separately.