In the Ni-Ti shape memory alloy system, Cu elements are used to replace Ni elements. A NiTiCu alloy with a molar ratio of 45:50:5 was prepared using laser selective melting technology. The density, composition, microstructure, and mechanical properties of the NiTiCu alloy were investigated. The results indicate that the highest density, exceeding 99.7%, was achieved when processing NiTiCu with parameters of 115 mm/s and 90 W. X-ray diffraction (XRD) analysis revealed that the primary phases of the sample are B2 and a minor amount of NiTi0.8Cu0.2. Energy-dispersive X-ray spectroscopy (EDS) observations of the NiTiCu alloy in the X-Y and X-Z planes show that Ni, Ti, and Cu elements are distributed nearly uniformly. Electron backscatter diffraction (EBSD) analysis revealed fine grain sizes, with grain sizes ranging from 140 μm to 160 μm. The X-Y plane predominantly exhibits equiaxed grains with a grain orientation between and , and a texture strength of 1.312; the X-Z plane predominantly exhibits columnar grains with grain orientations between and , and a texture strength of 1.427. The sample demonstrates good mechanical properties at room temperature, with a tensile strength of 375 MPa, exhibiting a ductile–brittle mixed fracture mode. The average microhardness is 240 HV for the X-Y plane and 235 HV for the X-Z plane.