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By using identity functional theory (DFT), optical properties of Cu-X(X=F, Ci, Br, I) co-doped anatase-TiO2 were investigated. The results reveal that Cu-X(X=F, Cl, Br, I) co-doped anatase TiO2 structures were easy to be formed because of the negative formation energies. Cu-X(X = F, Cl, Br, I) co-doped TiO2 reduced the band gap on the one hand, and on the other hand, the 3d state of Cu and the p-state electron of a halogen element formed a hybrid state in the forbidden band, which was beneficial to visible light, and prevented the re- combination of photogenerated corners and holes. Finally, Cu-X(X=F, Cl, Br, I) co-doped TiO2 led to red shift of the dielectric constant, absorption coefficient, refractive index and photoconductivity, which was beneficial to absorb visible light. [ABSTRACT FROM AUTHOR]