The geometrical structures, electronic structures, densities of states and optical properties of undoped ZnO, and Yb2+- and Yb3+-doped ZnO are calculated based on the first-principles density function theory pseudopotential method. The calculated results show that the system exhibits lower energy and better stability after the ytterbium incorporation, and a new localized band appears between the valance and conduct. The ytterbium with different valences has different influences on the electronic structure and optical properties. The imaginary parts of dielectric function of Yb2+- and Yb3+-doped ZnO both exhibit a new peak of 0.46 eV compared with that of undoped ZnO, Their static dielectric constants increase obviously, the absorption band edges are shifted toward the longer wavelengths, and strong absorption peaks appear at 0.91 eV. The reason for the phenomena is also discussed in this paper.