Al-Cu-Mg alloys are successfully fabricated by selective laser melting (SLM). The influence of the applied laser linear energy density on the densification behavior of SLM-processed samples is investigated. Microstructure and mechanical properties of the SLM-processed Al-Cu-Mg alloys are studied based on the nearly fully densified samples. Finally, the mechanical properties of the samples are improved by heat treatment. The results show that the nearly fully densified samples with the highest relative density of 99.8% can be obtained when the laser linear energy density is 2.4 kJ/m. The SLM-processed Al-Cu-Mg samples are constituted of ultrafine supersaturated cellular-dendrites. The tensile strength of 401 MPa, the yield strength of 252 MPa and the elongation of 6.5% are achieved for the SLM-processed Al-Cu-Mg samples in virtue of the effect of grain refinement and solid solution strengthening. After T4 heat treatment, under the effect of precipitation strengthening, the tensile strength increases to 532 MPa, the yield strength increases to 338 MPa and the elongation increases to 13%.