An aluminum alloy brazing sheet used for brazing aluminum, without using a flux, in an inert gas atmosphere or vacuum is formed by arranging a brazing material on one side or both sides of a core material made of pure aluminum or aluminum alloy, the brazing material including 6% to 13% by mass of Si and the balance being Al and inevitable impurities, and performing cladding with an intermediate material interposed between the core material and the brazing material, the intermediate material including 0.01% to 1.5% by mass of Bi, 1.5% to 13% by mass of Si, and the balance being Al and inevitable impurities, the intermediate material having a thickness of 2% to 35% of a thickness of the brazing material, wherein one or both of the intermediate material and the core material includes 0.4% to 6% by mass of Mg.