In the present invention, a fuel cell stack is configured by layering a plurality of fuel cell single cells, each having a membrane electrode joined body and a pair of separators sandwiching the membrane electrode joined body. This fuel cell stack seal structure comprises: an inner peripheral seal member plugging a gap between inner peripheral ribs, each protruding at least on the facing surface side of the pair of separators, at the peripheral edge portion of each of the separators; and an outer peripheral seal member plugging a gap between outer peripheral ribs, each protruding at least on the facing surface side of the pair of separators, at the outer peripheral side of the inner peripheral ribs. The inner peripheral seal member and the outer peripheral seal member form a first closed space between the inner peripheral seal member and the outer peripheral seal member. The outer peripheral seal member has a cut-out portion wherethrough the first closed space is in communication withthe exterior.