The optical properties of alpha-CuSe bulk and its nano-layers (NLs) have been studied by the first principles theoretical study in the framework of density functional theory. These properties are calculated with regard to dielectric function, refractive index, extinction coefficient, reflection coefficient, absorption coefficient, energy-loss function, and optical conductivity. To create NLs, two different thicknesses through CuSe bulk are chosen in the (0001) direction as the first and second thicknesses. The former thickness is divided into six different NLs with variant alternations. These NLs have the same chemical composition and are structural isomers. Among the NLs, the optical properties of the most stable NL and its double thickness are calculated and compared with the bulk state. The imaginary part of dielectric function has a main peak at low energies because alpha-CuSe is a conductive compound in the bulk state. The electronic structure of NLs shows that they have remained conductive in x (or y) direction, but they interestingly have a dielectric behavior with an ultra-low electrical conductivity in z direction. The optical curves in the bulk and NLs show the anisotropic feature between x and z directions. In the range of infrared to red light, the bulk refractive index, n(z)(omega), is very large, about 6, while n(x)(omega) is about 3. Results show that the NLs have wide absorption curves in the range of solar spectrum from infrared to ultraviolet. (C) 2014 Elsevier B.V. All rights reserved.