Concurrent precipitation in an age hardenable aluminum alloy determines recrystallization behavior especially grains structure and recrystallization texture during continuous heating. In this study, to investigate the effect of concurrent precipitation on the recrystallization texture and grains structure, a solution treated Al-Cu-Mg alloy has been multi-directionally forged at room temperature and continuously heated with different heating rates (800, 1600 and 2500 K·min−1) up to 450 °C using Gleeble 3800 thermo-mechanical simulator. At lower heating rates (800 K·min−1), Goss texture component {110} 〈001〉(Φ1 = 90°/0°, Φ=90°/45°, Φ2 =45°/90°) is developed during continuous heating and increasing the heating rate leads to gradual diminishing of Goss texture component. The results demonstrate that at lower heating rate, concurrent fine S′/S precipitation takes place during heating and increasing the heating rate hinders concurrent precipitation. The intensity of Goss texture depends on the extent of concurrent precipitation. The strong concurrent precipitation leads to strong Goss texture component, while without any precipitation there is no Goss texture and randomly orientated microstructure has been developed. The presence of low and high angle grain boundaries after heating at lower heating rate and concurrent precipitation of fine S′/S particles suggest that extended recovery occurs. The association of constituent large particles like Al7Cu2Fe and randomly orientated microstructure after heating at higher heating rate implies the occurrence of particle stimulated nucleation (PSN).