Owing to its high specific strength and low density, Al–Cu alloys have been extensively used in aerospace for lightweight components. Additive manufacturing techniques such as selective laser melting, which offers geometric freedom, is suitable for topology-optimized designs. In this study, the effect of processing parameters on the densification, microstructure, and mechanical properties of additively manufactured Al–Cu alloy 2124 by selective laser melting was investigated. Parameters such as laser power, scanning speed, hatch spacing, and use of a support were studied. The results revealed that a grille support with a hollow structure played a resistant role in the transfer of heat to the base plate, thus reducing the temperature gradient and lessening cracks in the building part. Smaller hatch spacing was beneficial for the achievement of a higher relative density and strength due to track re-melting and liquid phase backflow, which could fill cracks and pores during the building process. An ultimate tensile strength as high as 300 MPa of the vertically built sample was obtained at optimized processing parameters, while the elongation was relatively limited. Moreover, columnar grains were found to be responsible for the anisotropy of the mechanical properties of the as-printed 2124 alloy.