To improve the mechanical properties of aluminum alloys, Al-1Cu-1Mg-3Mn-0.8Sc-0.8Zr alloy was designed for selective laser melting (SLM) forming technology with a high cooling rate. In order to establish the best fabrication settings, the effect of SLM forming parameters on the designed alloy was studied and the mechanical properties of as-built alloy were evaluated. The orthogonal experiments revealed that the laser power and scanning speed are the key parameters affecting the densities and hardness of the alloy. According to the study of the effects of different processing parameters on defects, irregular metallurgical holes and cracks in the alloy increased with the decrease of the laser power and the increase of the scanning speed, while high laser power or low scanning speed would lead to large round holes in the alloy. The optimal fabrication parameters for Al-(Cu, Mg, Mn)-(Sc, Zr) alloy was determined as follows: laser power is 330 W, scanning speed is 900 mm/s, and hatch distance 0.12 mm. The alloy has a tensile strength of 349 MPa, a yield strength of 267 MPa, and an elongation of 7%.