A fuel cell module includes an anode flow board, a cathode board, an intermediate adhesive layer, a membrane electrode assembly (MEA) including a membrane edge, and a leak-proof adhesive layer mounted on the membrane edge, thereby preventing contact between the intermediate adhesive layer and the membrane edge. The adhesive ability of the leak-proof adhesive layer to the membrane edge is higher than that of the intermediate adhesive layer to the membrane edge. Therefore, the methanol leakage from the membrane can be avoided.