A method for forming a metal wiring structure includes: (i) providing a multi-layer structure including an exposed wiring layer and an exposed insulating layer in a reaction space; (ii) introducing an —NH2 or >NH terminal at least on an exposed surface of the insulating layer in a reducing atmosphere; (iii) introducing a reducing compound to the reaction space and then purging a reaction space; (iv) introducing a metal halide compound to the reaction space and then purging the reaction space; (v) introducing a gas containing N and H and then purging the reaction space; (vi) repeating steps (iii) to (v) in sequence to produce a metal-containing barrier layer; and (vii) forming a metal film on the metal-containing barrier layer.