A method is disclosed which comprises setting a substrate within a mixed gas atmosphere containing 0.1 to 5% of oxygen gas and a balance as an inert gas, and sputtering a target member containing Ln, M, Cu and O within that atmosphere to obtain an oxygen-deficient perovskite type oxide superconducting thin-film of substantially Ln:M:Cu:O=1:2:3:(7-.delta.), where Ln represents at least one element selected from the rare earth elements and M represents at least one element selected from the group consisting of Ba, Sr, and Ca. The oxide superconducting thin-film of that composition ratio has a critical temperature of over 77K.