In a MEA (membrane electrode assembly) of a fuel cell including an electrolyte membrane as an ion transfer medium arranged between a bipolar plate having a fuel side open groove in which fuel flows and a bipolar plate having an air side open groove in which air flows so as to form a fuel path with the fuel side open groove and form an air path with the air side open groove; and a catalyst electrode inserted into the fuel side open groove so as to be separated from the electrolyte membrane in order to form a fuel path with both sides thereof and induce electrochemical oxidation with the fuel, by activating action occurred on the fuel electrode in which fuel is supplied and the air electrode in which air is supplied, current generating efficiency can be improved.