The interest for a wider range of usable materials for the technology of selective laser melting (SLM) is growing. In this work, the manufacturing of wrought Al–Cu–Mg parts using SLM technology was systematically investigated. The effect of processing parameters on the density of the deposited Al–Cu–Mg samples was studied. It shows that the laser energy density plays a significant role in the densification behavior of the Al–Cu–Mg powder during the SLM process. The laser energy density value of 340 J/mm3 is found to be the threshold, above which high density samples (99.8%) without imperfections and microcracks can be obtained. The SLMed Al–Cu–Mg part presents a unique layer-wise feature which consisted of an extremely fine supersaturated cellular-dendrites structure. The ultimate tensile strength of 402 MPa and the yield strength of 276 MPa are achieved for the SLMed Al–Cu–Mg part. The combination of grain refinement and solid solution strengthening mechanisms during SLM process are proposed to explain the high mechanical strength.