A membrane electrode assembly structure of a fuel cell and a method of making the same are disclosed. The materials to be used include NiO, 8YSZ and 3YSZ that mixed into a slurry, formed into anodes by tape casting, sintered to form an anode substrate, and followed by forming a thin film of electrolyte layer on the surface of the anode substrate, forming a cathode layer on the outer surface of the electrolyte layer to obtain the membrane electrode assembly, which utilizes the 3YSZ having a tetragonal crystal phase to improve the toughness and mechanical strength of the material of NiO-8YSZ through calcination, thus the thickness of the anode substrate can be reduced, and the fuel gas diffusion path and resistance can be appropriately reduced to enhance the conductivity of the anode substrate.