A membrane-electrode assembly includes a catalyst layer formed on both sides of a polymer electrolyte membrane, a platinum (Pt)-metal alloy catalyst included in the catalyst layer, wherein the alloy catalyst shows a diffraction peak in a 110 plane at a degree of 2q =30-35 in the measurement of X-ray (CuK .alpha.) diffraction. The alloy catalyst has an excellent stability due to the compact crystal lattice structure of the catalyst, and it incurs low production costs and has sensitive reactivity.