An aluminum alloy sheet for motor vehicles is produced by casting a melt, containing 3.0-3.5 mass % Mg, 0.05-0.3 mass % Fe, 0.05-0.15 mass % Si, and less than 0.1 mass % Mn, a balance substantially being inevitable impurities and Al, into a slab having a thickness of 5 to 15 mm in a twin-belt caster so that cooling rate at ¼ depth of thickness of the slab is 20 to 200° C./sec; winding the cast thin slab into a coiled thin slab subjected to cold rolling with a roll having a surface roughness of 0.2 to 0.7 μm Ra at a cold rolling reduction of 50 to 98%; subjecting the cold rolled sheet to final annealing either continuously in a CAL at a holding temperature of 400 to 520° C. or in a batch annealing furnace at a holding temperature of 300 to 400° C.; and subjecting the resulting sheet to straightening with a leveler.