Additive Manufacturing (AM) of copper and its alloys is a promising way to produce parts with complex geometries without tooling. One of the AM processes is Selective Laser Melting (SLM) technology that uses a laser beam to fuse powder layers to obtain a final part. Laser processing of copper is considered to be a challenging task due to its high thermal conductivity and poor laser absorptivity. In the present work, Cu-Cr-Zr-Ti alloy powder has been utilized in the SLM process to produce bulk samples. SLM process parameters (laser power, scanning speed, hatch distance) have been optimized to achieve almost fully-dense samples with a relative density of about 99.2% and a smooth surface. The obtained bulk samples were used to evaluate the microstructure of the as processes Cu-Cr-Zr-Ti alloy, which consisted of elongated grains with the size of 30–250 µm. A test part built using the optimized SLM parameters was 3D-scanned to evaluate the dimension accuracy, which resulted in the average deviation of +88 μm / -81 μm from the CAD-model.