Provided is a fuel cell stack structure. The fuel cell stack structure includes first and second cell modules and first and second separation plates. In each of the first and second cell modules, one or more fuel cells generating electricity are stacked, and each of the fuel cells includes an electrolyte layer, and a cathode layer and an anode layer formed on both surfaces of the electrolyte layer, respectively, and generates electricity. The first and second separation plates are electrically connected to the first and second cell modules, respectively, and each separation plate has an air hole and a fuel hole at edges to provide an air including oxygen and a fuel gas including hydrogen to the cathode layer and the anode layer, respectively. At least one separation plate has a sealing unit for sealing the air hole and the fuel hole, and has a protruded convex at a different part from the sealing unit to improve an electrical contact with the other separation plate.