A melt which contains 3.0-3.5 mass% magnesium, 0.05-0.3 mass% iron, and 0.05-0.15 mass% silicon and has a manganese content reduced to below 0.1 mass%, with the remainder substantially being incidental impurities and aluminum, is cast into a thin slab having a thickness of 5-15 mm with a twin-belt casting machine under such conditions as to result in a cooling rate, as measured in a position corresponding to 1/4 the thickness, of 20-200 DEG C/sec. The cast is wound into a coil and then subjected to cold rolling with a roll having a surface roughness (Ra) of 0.2-0.7mu m at a cold rolling reduction of 50-98%. The slab rolled is subjected to final annealing either continuously in a CAL at a holding temperature of 400-520 DEG C or with a batch annealing oven at a holding temperature of 300-400 DEG C. The resultant sheet is subjected to stress relieving with a leveler. Thus, an aluminum alloy sheet for motor vehicles which is excellent in press formability, unsusceptibility to surface roughening, and shape fixability is provided without the need of a stabilization treatment.