An aluminum alloy brazing sheet having a core material of an aluminum alloy, and a filler material cladded on the core is disclosed. The core material is an aluminum alloy having about 0.05 to about 1.2 mass Si, about 0.05-about 1.0 mass % Fe, about 0.05-about 1.2 mass % Cu, and about 0.6-about 1.8 mass % Mn, balance Al and the inevitable impurities. The filler material includes an aluminum alloy having about 2.5-about 13.0 mass % Si. Also, there is provided a method of manufacturing such an aluminum alloy brazing sheet.