The electronic and optical properties of the ternary CuXY2 (X = In, Ga, Al; Y = S, Se, Te) compounds have been investigated using the density functional theory based on the full potential linear augmented plane wave method via Tran-Blaha-modified Becke-Johnson exchange potential techniques. From this study, it is found that these compounds are direct band gap semiconductor and in good agreement with reported results. The optical properties such as dielectric tensor components and the absorption coefficient of these materials are determined in order to investigate their usefulness as solar cell materials.