A composite multi-core wire rod in which a plurality of Al alloy wires containing 15 at % to 40 at % of Ge are arranged in Nb matrix at a core diameter of 2 μm to 20 μm is subjected to heating for at least five hours at a temperature ranging from 1300° C. to 1600° C.; and additionally heating at a temperature ranging from 650° C. to 900° C.