Fault diagnosis is a key process for the reliability and safety of solid oxide fuel cell (SOFC) systems. However, it is difficult to rapidly and accurately identify faults for complicated SOFC systems, especially when simultaneous faults appear. In this research, a data-driven Multi-Label (ML) pattern identification approach is proposed to address the simultaneous fault diagnosis of SOFC systems. The framework of the simultaneous-fault diagnosis primarily includes two components: feature extraction and ML-SVM classifier. The simultaneous-fault diagnosis approach can be trained to diagnose simultaneous SOFC faults, such as fuel leakage, air leakage in different positions in the SOFC system, by just using simple training data sets consisting only single fault and not demanding simultaneous faults data. The experimental result shows the proposed framework can diagnose the simultaneous SOFC system faults with high accuracy requiring small number training data and low computational burden. In addition, Fault Inference Tree Analysis (FITA) is employed to identify the correlations among possible faults and their corresponding symptoms at the system component level.