Fault diagnosis technology is a vital tool for ensuring the stability and durability of solid oxide fuel cell systems. Simultaneous faults are common problems in modern industrial systems. Many fault diagnosis methods have been successfully designed for solid oxide fuel cell systems, but they only address independent faults, and only a few researchers have studied simultaneous fault diagnosis. The design of a simultaneous fault diagnosis method for solid oxide fuel cell systems remains a huge challenge. This study introduces a deep learning technology into the simultaneous fault diagnosis for the solid oxide fuel cell system and proposes a novel simultaneous fault diagnosis method on the basis of a deep learning network called stacked sparse autoencoder. The proposed method can automatically capture the essential features from the original system variables, thereby consuming minimal time on heavily hand-crafted features. Moreover, massive unlabeled samples are fully utilized through the proposed method. Experimental results show that the proposed method can diagnose simultaneous faults with high accuracy requiring only a few independent fault samples and a minimal number of simultaneous fault samples. Comparisons between traditional machine learning methods and experimental results on training sets of different sizes verify the superiority of the proposed method. Deep learning provides an effective and promising approach for simultaneous fault diagnosis in the field of fuel cells.