Disclosed is an aluminum alloy brazing sheet for heat exchanger which excels in resistance to corrosion from its inside and simultaneously attains satisfactory erosion resistance and high strength. This includes a core material of an Al alloy containing predetermined amounts of Si, Mn, Cu, Mg, and Ti; a clad material of an Al alloy containing predetermined amounts of Si, Mn, and Zn, having a predetermined thickness, and lying on one side of the core material so as to constitute an inner side of a tube member of the heat exchanger; and a filler material of an Al alloy containing a predetermined amount of Si, having a predetermined thickness, and lying on the other side of the core material so as to constitute an outer side of the tube member. The crystal grain size of the core material after brazing under specific conditions is 50 μm or more but less than 300 μm in a rolling direction.