The purpose of this study was to investigate the effect of carbon nanotube addition on the microstructure and mechanical properties of Al–Cu–Mg alloy composites. By analyzing the XRD results, it was deduced that the extruded and heat-treated composites, after the addition of CNTs, were preferentially grown on the (220) crystal plane. In addition, the distribution of carbon nanotubes at α-Al grain boundaries was observed by SEM and TEM. The incorporation of carbon nanotubes leads to an increase in the degree of recrystallization in the composite. It is worth noting that according to the study of the four strengthening mechanisms of dislocation strengthening, grain refinement strengthening, load transfer strengthening, and second stage strengthening, when the carbon nanotube content is 1.5 wt.%, the tensile strength (480.4 MPa) and yield strength (456.68 MPa) are significantly improved.