The invention aims at providing heat-treatable high-strength Al-Cu-Mg-Si aluminum-base alloy products which exhibit both excellent extrudability and high strength. An Al-Cu-Mg-Si aluminum-base alloy product obtained by extrusion, characterized in that the microstructure of the whole section of the extruded product is constituted of recrystallized grains having a mean aspect ratio (L/t) of 5.0 or below (wherein L is mean grain diameter of the grains in the direction of extrusion and t is mean thickness of the grains) and that in the texture, the orientation density of grains where the normal lines of {001} plane are parallel to the direction of extrusion is at most 50 times that of random orientation; and an Al-Cu-Mg-Si aluminum-base alloy product obtained by extrusion and cold working, characterized in that rod-like precipitates having an average length of 10 to 70nm and the maximum length of 120nm or below are arranged in the matrix grains in direction at a number density in [001] direction of 500 pieces/[mu]m<2> or above as determined in the visual field of observation from (001) plane.