The electronic structure and optical properties of Sb doped ZnO, together with the corresponding results of pure ZnO for comparison, were systematically studied from the first principles based on density functional theory. The calculated results show that for ZnO doped with Sb, the lattice constant, bond length, primitive cell volume and total energy are all larger than those of pure ZnO. For the doping case, the Fermi level becomes larger than the conduction band minimum (CBM), the system grows metallic and the band gap becomes wider. For the optical properties, a new absorption peak appears near the main peak, which is mainly attributed to the transition of orbital electrons of Zn-4s and Sb-5p. Finally, it is also pointed out that for the dielectric function, the peak values of imaginary part and the static dielectric constant ε(0) value of real part become larger.