The flux-cored welding wire is intended to inert-gas shielded fusion welding of titanium and its alloys and includes a metal coating or tubular casting of titanium or its alloys and a powder flux core containing (per cent by weight): Baf2 -- 5 to 10, Fluoride of a rare-earth element -- 18 to 20, Caf2 -- 40 to 50, Srf2 -- the rest, The ratio of the weight content of the powder flux to the total weight content of titanium in the wire being from 0.3: 1 to 1: 1.