Based on the rst-principles plane-wave norm conserving pseudopotential of the spin-polarized density functional theory(DFT), we determined the U value of each atom for the Zn16O16 supercell via the method of generalized gradient approximation(GGA+U). The stability of the mixed structure is analyzed by calculating the formation energy and chemical bond Population. The energy band structure and the magnetic state of each doped structure is analyzed by calculating the atomic charge Population and spin electronic state density. Finally The effects of each rare earth element on the absorption spectrum of ZnO are discussed. The calculated results show that the lattice is expanded by the introduction of rare earth elements, the longest Zn-O bond increases and the shortest Zn-O bond decreases, which leads to distortion of oxygen tetrahedron. Y/La/Ce doped ZnO possesses ferrimagnetism, Th doped ZnO exhibits weak ferromagnetism, and Ac doped ZnO is paramagnetic body. Rare earth elements make the valence band and conduction band of ZnO down, make Fermi energy level enter the conduction band, and meanwhile enhance the conductivity of the system. The effect of Y/La /Ca doping on the ZnO band-gap is small, and the absorption spectrum is slightly blue-shifted, while visible light absorption coefficient of ZnO is effectively improved because Ce/Th is doped.