By using the first principle pseudo-potential plane-wave method based on the density function theory (DFT), the geometrical structure, electronic structure and optical properties of β-FeSi2 with doping Ac are calculated and analyzed. The calculated results of the geometrical structure show that the lattice constants a, b and c change, the volume of lattice expands. Electronic structure calculation indicates that the Fermi energy moves to conduction band, the band structure is still quasi-direct bandgap, which becomes narrow obviously. The density of state near the Fermi energy level is mainly composed of Fe-3d and Si-3p, Ac-6d only devoted to a small part. Optical properties calculation indicates that the static dielectric constant ε1(0) increases. The peak of the imaginary part of dielectric function ε2 decreases and moves to a lower energy. The refractive index n0 increases significantly and k moves to a lower energy. Optical absorption coefficient increases. The average reflective effect has little change. These results offer theoretical data for doping of β-FeSi2.