Al-Ni-Cu alloys are used in energy, automotive, and aerospace industries because of their excellent mechanical properties, corrosion resistance, and high-temperature stability. In this study, Al-Ni-Cu alloy powder was subjected to selective laser melting (SLM). The SLM Al-Ni-Cu alloy was manufactured using appropriate printing parameters, and its properties were investigated. The results revealed that the As-printed material exhibited a typical melting pool stack structure, with an ultimate tensile strength of 725 MPa but a high brittleness effect (low ductility). After traditional heat treatment, the melting pool structure did not completely disappear. The strengthening phase Al7Cu23Ni precipitated from the boundary of the melting pools; thus, the Al-Ni-Cu alloy maintained high strength (>500 MPa) and considerably increased ductility (>10%). The SLM Al-Ni-Cu alloy has considerable industrial application potential; therefore, increasing the heat treatment temperature or extending the heat treatment time in the future works can promote the decomposition of the melting pool boundary and solve the problem related to the aggregation behavior of the precipitation phase, thereby improving the fatigue life of the alloy.