PURPOSE: To increase superconducting critical temp. without incorporating Cu by incorporating a specified compd.

CONSTITUTION: The carbonate of a monovalent metallic element (α) selected among Li, Na and K is mixed with the oxide of a di- to pentavalent metallic element (γ) selected among the groups IIA, IIIA, IVA and VA elements of the periodic table and the oxide of at least one kind of transition element (β), e.g. TiO2 and the mixture is press-molded and temporarily sintered in gaseous oxygen to remove carbon. The temporarily sintered body is crushed, an oxide contg. the element β is added to the resulting powder and they are press-molded and conclusively sintered in an inert atmosphere to obtain an oxide superconducting material contg. a compd. represented by a formula (α γ)β2O4.