A method includes: preparing a molten aluminum alloy consisting of 0.3-0.8 mass % Mg, 0.5-1.2 mass % Si, 0.3 mass % or more excess Si relative to the Mg2Si stoichiometric composition, 0.05-0.4 mass % Cu, 0.2-0.4 mass % Mn, 0.1-0.3 mass % Cr, 0.2 mass % or less Fe, 0.2 mass % or less Zr, and 0.005-0.1 mass % Ti, with the balance being aluminum and unavoidable impurities; casting the alloy into a billet at a speed of 80 mm/min or more and a cooling rate of 15° C./sec or more; extruding the billet into an extruded product; water cooling the product immediately after extrusion at 500° C./min or more; and artificially aging the product, thereby yielding an extruded product with fatigue strength of 140 MPa or more, fatigue ratio of 0.45 or more, an interval between striations on a fatigue fracture surface of 5.0 μm or less, and a maximum length of Al—Fe—Si crystallized products of 10 μm or less.