An oxide superconductor composed of Cu, O and at least one of Ba, Sr and Ca and including alternately arranged at least one oxygen-deficient perovskite structure section and at least one infinite layer structure section, wherein the perovskite structure section consists of two first atomic layers and a second atomic layer sandwiched between the first layers, and wherein the infinite layer structure section consists of alternately arranged, third and fourth atomic layers. Each of the first layers consists of O and an element M.sup.1 selected from Ba, Sr and Ca and has an atomic ratio O/M.sup.1 of 1 or less, while the second layer consists of O and Cu and has an atomic ratio O/Cu of 2 or less. Each of the third layers consists of O and Cu and has an atomic ratio O/Cu of 2, while each of the fourth layers consists of an element M.sup.2 selected from Ba, Sr and Ca. A superconductor having a superconducting critical temperature of over 100 K. may be produced by heat treatment at 800.degree.-1,200.degree.C. under a super-high pressure of 20,000-80,000 atm.