Different compositions of amorphous Ge15Se85-xCux thin films were deposited onto glass substrates by the thermal evaporation technique. Their amorphous structural characteristics were studied by X-ray diffraction (XRD). The optical constants (n, k) of amorphous Ge15Se85-xCux thin films were obtained by fitting the ellipsometric parameters (ψ and Δ) data for the first time using three layers model system in the wavelength range 300–1100 nm. It was found that the refractive index, n, increases with the increase of Cu content. The possible optical transition in these films is found to be indirect transitions. The optical energy gap decreases linearly from 1.83 to 1.44 eV with increasing the Cu. The experimental transmittances spectrum can be simulated using the thickness and optical constants modeled by spectroscopic ellipsometry model.