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The electronic structure, magnetic properties and optical properties of anatase TiO2 and Cr doped anatase TiO2 ( 1/8, 1/16, 1/32) were studied by first principles GGA + U method. The calculation results show that the binding energy of Ti 0. 9375 Cr0. 0625 O2 is the smallest in all doping systems. Therefore, the stability of Ti 0. 9375 Cr0. 0625 O2 system is higher than that of Ti0. 875 Cr0. 125 O2 and Ti0. 96875 Cr0. 03125 O2, the doping of Cr leads to lattice distortion, which is beneficial to the separation of photogenerated holes and electron pairs, and improves the photocatalytic performance. At the same time, because of the interaction of Cr - 3d and 0 - 2p electrons, the doped system presents ferromagnetic properties, and with the increase of doping concentration, the system will have better ferromagnetic properties. Compared with the intrinsic TiO2, the absorption band edge of the doped system is red shifted and the spectral response range is enlarged, Moreover, with the increase of doping concentration, the light response range also increases, which effectively enhances the absorption ability of the system for visible light. [ABSTRACT FROM AUTHOR]