PURPOSE: To improve the strength and brightness after fabric grinding or machining-chemical grinding-anodic oxidation treatment in an aluminum alloy rolled sheet without deteriorating the stress corrosion resistance of a Cu-Mg aluminum alloy.

CONSTITUTION: This method for producing a high strength aluminum alloy rolled sheet excellent in brightness and stress corrosion cracking resistance is the one in which a rolled sheet obtd. by heating to 400 to 500°C an aluminum alloy ingot having a compsn. contg., by weight, 3.0 to 4.0% Mg and 0.3 to 0.7% Cu, in which, in addition to the same, as impurities, ≤0.10% Fe, ≤0.10% Si and <0.05% Mn are regulated, and the balance Al with inevitable impurities are contained, thereafter, subjecting the same to hot rolling and, if required, furthermore, executing cold rolling to regulate its sheet thickness to a required one, is heated within the temp. range from the solid solution limit temp. of an Al-Mg-Cu precipitation obtd. from the adding ratio of Mg and Cu shown by the figure to 500°C and is immediately, or after being held, subjected to softening treatment by rapid cooling at ≥5°C/sec temp. decreasing rate.