An aluminum brazing sheet has a core material made of an aluminum alloy and a cladding material cladded on at least one side of the core material and made of an aluminum alloy having a potential lower than that of the core material. The cladding material is made of an aluminum alloy consisting essentially of 0.4 to 0.7 mass % of Mg, 0.5 to 1.5 mass % of Si, and 0.4 to 1.2 mass % of Mn, the remainder being Al and unavoidable impurities. Zn in the amount of 6 mass % or less is added in accordance with need. An aluminum brazing sheet having not only high strength but also less pressure adhesion failure and excellent productivity can be obtained.