Provided are a solid electrolyte membrane useful in achieving strong electromotive force in a fuel battery, and a fuel battery cell produced with this membrane. The solid electrolyte membrane includes a substrate made of a sheet material and having a plurality of openings penetrating the substrate in its thickness direction, and a solid electrolyte layer provided on at least one of the faces of the substrate. The fuel battery cell includes a solid electrolyte membrane having the solid electrolyte layer on one of the faces of the substrate, and a catalyst layer containing a precious metal and provided on the other of the faces of the substrate, with the solid electrolyte layer and the catalyst layer being in contact with each other in the openings of the substrate.