An aluminum alloy heat exchanger is produced by applying a coating material that is prepared by adding a binder to a mixture of an Si powder and a Zn-containing compound flux powder to a surface of an aluminum alloy refrigerant tube, assembling a bare fin that is formed of an Al—Mn—Zn alloy with the refrigerant tube, and brazing the refrigerant tube and the bare fin by heating in an atmosphere-controlled furnace, the refrigerant tube being an extruded product of an aluminum alloy that comprises 0.5 to 1.7% (mass %, hereinafter the same) of Mn, less than 0.10% of Cu, and less than 0.10% of Si, with the balance being Al and unavoidable impurities, a mixing ratio of the Si powder to the Zn-containing compound flux powder being 10:90 to 40:60, the binder being added in an amount of 5 to 40% based on the total amount of the coating material, the coating material being applied to an outer surface of the refrigerant tube so that the total amount of the Si powder and the Zn-containing compound flux powder is 5 to 30 g/m2, the surface of the refrigerant tube subjected to brazing having a potential lower than that of an area of the refrigerant tube that is deeper than a diffusion depth of Si and Zn by 20 to 200 mV, and a potential of the fin being lower than that of a deep area of the refrigerant tube.