The fabrication of high-performance copper alloys by selective laser melting (SLM) is challenging, and establishing relationships between the process parameters and microstructures is necessary. In this study, Cu–Cr–Nb–Ti alloy is manufactured by SLM, and the microstructures of the alloy are investigated by X-ray diffraction (XRD), scanning electron microscope (SEM), and electron backscatter diffraction (EBSD). The effects of processing parameters such as laser power and scanning speed on the relative density, defects, microstructures, mechanical properties, and electrical conductivity of the Cu–Cr–Nb–Ti alloy are studied. The optimal processing window for fabricating Cu–Cr–Nb–Ti alloy by SLM is determined. Face-centered cubic (FCC) Cu diffraction peaks shifting to small angles are observed, and there are no diffraction peaks related to the second phase. The grains of XY planes have a bimodal distribution with an average grain size of 24–55 μm. Fine second phases with sizes of less than 50 nm are obtained. The microhardness, tensile strength, and elongation of the Cu–Cr–Nb–Ti alloy manufactured using the optimum processing parameters, laser power of 325 W and scanning speed of 800 mm/s, are 139 HV0.2, 416 MPa, and 27.8%, respectively, and the electrical conductivity is 15.6% IACS (International Annealed Copper Standard). This study provides a feasible scheme for preparing copper alloys with excellent performance and complex geometries.