TiO2 is a versatile functional material in consumer products, such as fabrication of solar cells, light hydrolysis of hydrogen production and optical coating. Technologically, the absorption edge of TiO2 is in the ultraviolet (UV) region, which restrics its applications. Cu doping can solve the crucial problem and extend the absorption edge from the UV to the visible region. The first-principle calculation based on density functional theory with generalized gradient approximation and ultra-soft pseudo-potentials is carried out to investigate the defective rutile TiO2 through using the constructed 222 supercells in which all atoms are allowed to relax. The plane-wave cutoff energy is 340 eV by selecting 223 of k-point in Brillouin zone. O vacancy, Ti vacancy, Cu interstitial, Cu substitutional for Ti and compound defects are all considered. After the structural relaxation, the lattice host is slightly distorted with a little change of the lattice parameters, with out affecting the crystalline phase of rutile. The results show that the valence bands are mostly O 2p states while the conduction bands have mainly Ti 3d properties. The defect of Cu interstitial can bring about two new impurity levels in the energy gap because of Cu 3d states, and the defect of Cu substituted for Ti can also induce two new impurity levels while they are next to the valence band due to the interaction between Cu 3d and nonbonding orbits of O 2p. Ti vacancy can cause the Fermi level energy to lower and produce a new impurity level at the top of the valence band, which will narrow the energy gap. O vacancy can enhance the Fermi level energy and produce a new level at the bottom of the conduction bands, which shows the n-type semiconductor properties. The higher the concentration of Cu substituted for Ti, the larger the band gap is. It is due to the strong interaction between Ti 3d and Cu 3d, which makes the conduction band move to higher energy. Different compound defects have different influences. Cu interstitial and O or Ti vacancies induce new impurity levels within the band gap, which narrows the gap. Meanwhile, interstitial Cu and vacancies can also interact with each other. The hybridization between Cu 3d and nonbonding orbits of O 2p will induce new levels in the rutile with Ti vacancy structure, while nonbonding orbits of Cu 3d develop new levels by itself in the rutile with O vacancy and Cu interstitial. The Analysis the band structure of rutile with compound defects, shows that the rutile with O vacancy and Cu interstitial effectively affects influenced the absorption edge in visible light range. Cu interstitial, Cu substituted for Ti, O vacancy, Ti vacancy and compound defects can all narrow the band gap and produce a new absorption peak in the visible spectral range. It indicates that rutile with defects will improve the absorption in the visible range and achieve the goal of expanding the absorption range of single-crystal rutile.