Recently, a new polymorph of the highly energetic phase β-CuN₃ has been synthesized. By hybrid density functional computations, we investigated the structural, electronic and optical properties of β-CuN₃ bulk and layers. Due to the quantum confinement effect, the band gap of the monolayer (2.39 eV) is larger than that of the bulk (2.23 eV). The layer number affects the configuration and the band gap. β-CuN₃ shows both ionic and covalent characters, and could be stable in the infrared and visible spectrum and would decompose under ultraviolet light. The results imply that bulk β-CuN₃ could be used as an energetic material.