A method of producing cladding tube comprises a step of temperature-gradient annealing in which the inner surface of the tube is heated to a temperature higher than the recrystallization temperature thereof, while the outer surface of the tube is cooled, after the tube has been hot-extruded. The temperature-gradient annealing is effected while a temperature gradient is maintained between the inner surface and the outer surface of the cladding tube. While keeping the inner surface at a temperature higher than the recrystallization temperature, and the outer surface at a temperature lower than the recrystallization temperature. The cladding tube is obtained with the outer surface which has an excellent resistance to nodular corrosion and a soft inner surface which has an excellent resistance to stress corrosion cracking.