A production method for producing a fuel cell, includes spinning a precursor consisting of a salt of at least one metal chosen from Sc, Y, La, Ce, Pr, Nd, Sm, Gd, Dy, Ho, Yb, Sr, Ba, Mn, Co, Mg, and Ga, a solvent, and a macromolecular polymer to produce nanofibers of the precursor containing the salt of the metal. The method further includes calcining the nanofibers of the precursor at a temperature ranging from 550° C. to 650° C. for 2 to 4 hours, and making a solid electrolyte material composed of the nanofibers obtained from the calcining. The resulting solid electrolyte material constitutes a part of a fuel cell.