The solid oxide fuel cell (SOFC) is a new energy technology that has the advantages of low emissions and high efficiency. However, oscillation and propagation often occur during the power generation of the system, which causes system performance degradation and reduced service life. To determine the root cause of multi-loop oscillation in an SOFC system, a data-driven diagnostic method is proposed in this paper. In our method, kernel principal component analysis (KPCA) and transfer entropy were applied to the system oscillation fault location. First, based on the KPCA method and the Oscillation Significance Index (OSI) of the system process variable, the process variables that were most affected by the oscillations were selected. Then, transfer entropy was used to quantitatively analyze the causal relationship between the oscillation variables and the oscillation propagation path, which determined the root cause of the oscillation. Finally, Granger causality (GC) analysis was used to verify the correctness of our method. The experimental results show that the proposed method can accurately and effectively locate the root cause of the SOFC system’s oscillation.