Fault diagnosis plays an important role in the operation of proton exchange membrane fuel cell (PEMFC) systems. In some certain working conditions, multiple faults can occur simultaneously. And, to the best of our knowledge, very few studies have yet to design an algorithm specifically for simultaneous fault diagnosis in PEMFC systems. Therefore, a novel simultaneous fault diagnosis algorithm, based on multi-label classifier chain named Incremental Multi-label Classification Network (IMCN), is proposed. To develop and optimize IMCN, a PEMFC model is constructed based on the commercial software AVL CURISE M to simulate data when simultaneous multiple faults occur. To further verify the generalization performance and practical effect of IMCN, a bench experiment using a high-power PEMFC system is conducted, which has similar boundary conditions as the boundary conditions embedded in simulation model. And, whether in experiment or simulation, corresponding verification methods are adopted to verify the success of simultaneous multiple faults embedding. Experimental data testing shows that, the subset accuracy, Hamming loss, Jaccard index, precision and recall of IMCN reaches 0.973, 0.029, 0.921, 0.961 and 0.956 respectively (better than Multi-Label MLP classifier, Label powerset MLP classifier, etc.), and the proposed simultaneous fault diagnosis method has achieved excellent results. • A method named Incremental Multi-label Classification Network (IMCN) is proposed. • Simultaneous fault diagnosis of PEMFC is realized through IMCN. • Three chain connected multi-layer perceptrons diagnose simultaneous faults jointly. • AVL CRUISE M is used to generate simulative data for developing IMCN. • An over-160kW PEMFC system is used for simultaneous fault data production.