A brazing sheet for brazing in an inert-gas atmosphere without using a flux has a core and a filler material clad to one side or both sides of the core. The core has a chemical composition that contains Mg: 0.35-0.8% (mass %; likewise hereinbelow), the remainder being composed of Al and unavoidable impurities. The filler material has a chemical composition that contains Si: 6-13% and Bi: 0.001-0.05% and Mg: limited less than 0.05%, the remainder being composed of Al and unavoidable impurities.