First principles calculations have been performed to investigate the structure, electronic and optical properties of Y 3 Fe 5 O 12 . Both the cubic and trigonal phases have been considered in our calculation. The calculated structural parameters are slightly larger than the experimental values. The band structures show that Y 3 Fe 5 O 12 in cubic and trigonal phases have direct band gaps of 0.65 and 0.17 eV. The calculations of dielectric function, absorption, extinction coefficient, refractive index, energy loss function and reflectivity are presented.