Abstract: The present invention provides a method by which an oxide material having excellent thermoelectric conversion performance can be produced by a simple process. Specifically, the present invention provides a method for producing a composite oxide single crystal in which a mixture of raw substances including a Bi-containing substance, a Sr-containing substance, a Ca-containing substance, a Co-containing substance and a Te-containing substance, or a mixture of raw substances also including a Pb-containing substance in addition to the above-mentioned substances, is heated in an oxygen-containing atmosphere at a temperature below the melting point of any of the raw substances. The composite oxide single crystal produced by the method of the present invention is a ribbon-shaped fibrous single crystal that is about 10 to 10,000 ?m long, about 20 to 200 ?m wide, and about 1 to 5 ?m thick.