In this paper we use first-principles full potential linearized augmented plane wave method to investigate the band structure, density of states as well as the optical properties of ZnO, intrinsic and doped separately with Er and Gd. We find that dut to the carriers contributed by the introduced impurity atoms of rare earth (RE), the electrical conductivity of the system is improved and the Fermi level has an upward shift to the conduction band. The data show that due to the doping of RE, there appear the new electron occupied states around the Fermi level. This is formed by the states of Er-4f and Gd-4f. Meanwhile, intrinsic ZnO and doped structures are obviously different. For the optical properties, the absorption coefficient and reflectivity of rare earth doped ZnO are higher than those of intrinsic ZnO in visible region and the energy loss spectra of RE doped ZnO structure present red-shift.