A Mg-doped high-temperature superconductor, comprising a two dimensional layered structure constituted by a charge reservoir layer and a superconducting layer, wherein some or all atoms comprising the charge reservoir layer are Cu and O atoms, metallizing or rendering the charge reservoir layer superconducting, and a portion of Ca of CunCan−1O2n constituting the superconducting layer is replaced by Mg, and comprises a copper oxide superconductor having a composition expressed by a formula Cu1−xMx(Ba1−ySry)2(Ca1−zMgz)n−1CunO2n+4−w (in which M is at least one selected from a group consisting of Tl, Hg, Bi, Pb, Au, In, Sn, Mg, Ag, Mo, Re, Os, Cr, V, Fe, and lanthanide elements, 0≦x<1, 0≦y<1, 0<z<1, 0≦w≦4,and 3≦n≦16).