A composite member is prepared which comprises a core which will have a compound superconducting layer when heat-treated, and a stock for forming a stabilizing member made of copper and surrounding the core. The composite member is heat-treated in an oxidizing atmosphere, thus forming a copper-oxide thin layer on the surface of the stock. Thereafter, the composite member is heat-treated in a non-oxidizing atmosphere or in an atmosphere having an oxygen partial pressure which is too low to allow the forming of copper oxide. As a result, a compound superconducting wire is made which comprises a member including a compound superconductor, a diffusion-preventing layer made of oxide and surrounding the member, and a stabilizing member made of copper and surrounding the layer.