The models of pure TiO2 and La/Ce/Pr/Nd singly doped TiO2 are established by using the plane wave potential based on density functional theory. After geometry optimization, the stability of the mixed structure is analyzed by calculating the formation energy. Then the magnetic state of each doped model is analyzed by calculating the spin electronic state density. The analyses are verified by comparing magnetic ground state energies. Finally the influences of each rare earth element on band structure and absorption spectrum of TiO2 are discussed. The results show that La/Pr doped TiO2 presents ferromagnetism, Nd doped TiO2 exhibits anti-ferromagnetism, and Ce doped TiO2 is paramagnetic body. The band structure of TiO2 is affected less because Ce is doped and the red shift of absorption spectrum is not obvious. While visible light absorption coefficient of TiO2 is effectively improved because La/Nd is doped. Pr doped TiO2 manifests an absorption peak in the infrared region. If the electronic structure is considered in the further calculation research, one should make sure what magnetic state the system is in and whether there is spin-electron band splitting effect firstly. In order to obtain the correct results, the influence of the band structure should not be ignored.