Ti_(4)O_(8) super cell are formated and geometry optimized.The band gap, Fermi level, density of states of TiO_(2) doped by Fe(III) have been simulated with relativistic density functional theory and Plane Wave Pseudo Potentials (PWPP). The band gap of TiO_(2) doped by Fe(III) become narrow, and density of states are enhanced. It can decrease composition of e~(-) and h~(+), Photocatalytic activity of TiO_(2) are enhanced by doped Fe(III).