A high temperature fuel cell system having a cooling apparatus, including: a fuel cell stack including a plurality of membrane electrode assemblies (MEAs) each having an anode electrode and a cathode electrode on opposing surfaces of an electrolyte membrane containing acid and a plurality of conductive plates contacting each electrode; an anode inlet line, which is connected to the fuel cell stack, and which supplies a hydrogen containing gas to the anode electrode; an anode outlet line, which is connected to the fuel cell stack, and which discharges byproducts produced at the anode electrode along with un-reacted hydrogen containing gas; a cathode inlet line, which is connected to the fuel cell stack, and which supplies oxygen to the cathode electrode; a cathode outlet line, which is connected to the fuel cell stack, and which discharges byproducts produced at the cathode electrode along with un-reacted oxygen; a cooling apparatus, which is installed at the anode inlet line, and which reduces a temperature of the hydrogen containing gas; and a moisture removing device that removes moisture from the hydrogen containing gas.