Solid oxide fuel cell (SOFC), characterized by their clean, pollution-free nature and high power generation efficiency, hold great potential for widespread application. However, faults in SOFCs can severely impact their performance, shorten their lifespan, and undermine their reliability in practical use. To address these challenges, this study proposes a novel diagnostic method based on a convolutional neural network (CNN) and support vector machines (SVM). Initially, data involving 10 feature variables corresponding to three types of faults—hydrogen leakage, air leakage, and stack performance degradation—were collected. CNN was employed to extract the feature information from the data, which was subsequently fed into SVM for fault diagnosis. Comparative analyses were conducted under identical conditions using alternative diagnostic methods. Experimental results demonstrated that the CNN-SVM model outperformed standalone CNN and SVM approaches, improving diagnostic accuracy by 5.82% and 13.03%, respectively. Compared to SNN, the CNN-SVM model achieved a 0.88% increase in accuracy while exhibiting a faster processing speed, with a runtime of only 3.02 s. The study aims to provide a highly accurate and responsive diagnostic method for SOFC system fault detection.