Fault diagnosis has been considered as a crucial technique that the commercial fuel cell systems should be equipped with. Knowing that different faults or functioning modes can cause different distributions of current densities, monitoring the current density for fuel cells could be a possible solution to realize fault diagnosis. In the previous studies, a non-intrusive current density estimation method has been developed by measuring the magnetic fields around the fuel cells. However, a clear quantitative diagnosis strategy was not provided in these studies. This paper is dedicated to study a quantitative data-driven diagnosis strategy based on the magnetic measurement. In the proposed strategy, fault diagnosis can be realized by a two-step procedure, i.e., feature extraction and classification. The high diagnosis performance on the detection and identification of several common faults highlights the effectiveness of the proposed strategy. In addition to the basic diagnosis function, an index is proposed to quantify the faulty level as a fault is diagnosed. The proposed strategy is also compared with the ones in the literature to show its pros and cons.