Cu doped TiO₂ can help to understand the magnetic origin of TiO₂-based diluted magnetic semiconductors. As such, herein, we calculated the systems of TiO₂ with different valence states and concentrations of Cu substituted for Zn as well as Cu substitution and vacancy complex defects. For the substitution ratio of 1/48, ferromagnetism appears only in Cu⁰ substitution system. By increasing the concentration of Cu to 1/24, Cu²⁺ substitution system also shows a ferromagnetic ground state when the Cu substitutions are not separated by empty regions (low charge density regions) and along the (111) direction. The Cu substitution and oxygen vacancy complex defect systems are easily polarized due to carriers induced by vacancy. Carriers change the bond of Ti ions around the defect, and arouse residual magnetic moment; however, the contribution of carriers to the electronic structure had a saturation limit. Oxygen vacancy leads to the formation of non-ferromagnetic coupling between two Cu substitutions in a 2 × 2 × 2 supercell. Cu substitution and Ti vacancy composite defect give rise to the weakening of p–d hybridization, and the lattice distortion caused by defects and the strong interaction of Cu–O bond is the source of ferromagnetism. The room-temperature ferromagnetism in Cu doped monocrystalline TiO₂ samples could be mediated by vacancies or carriers.