A novel methodology combining the macro- and micro-creep techniques was employed to study the effect of S′/S precipitate growth on the creep mechanism of an Al–Cu–Mg alloy. An AA2524 alloy was pre-aged at 180 °C to obtain S′/S precipitates with various sizes. The results showed that the precipitate size increased approximately linearly to ≈32 nm, ≈60 nm, and ≈105 nm after 3 h, 6 h, and 12 h of pre-aging, respectively. The growth of precipitate could significantly shorten the primary creep stage, despite the fact that the steady-state creep behavior was similar to that of the as-received alloy, as revealed by the macro tensile creep tests at 180 °C and 180 MPa. This led to a stress exponent (2.4–2.5) of the Al alloy with various precipitate sizes that was quite close to that of the as-received Al alloy, implying a steady-state creep mechanism dominated by grain boundary sliding and dislocation interactions. Finally, the micro-creep tests showed a minor role of the precipitate size on the steady-state creep mechanism, as evidenced by the similar strain rate sensitivity (0.0169–0.0186), activation volume (≈27 b3), and the results of a detailed transmission electron microscopy analysis of all tested alloys.