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The geometric structures of perfect ZnTe, that with Zn vacancy (Zn0.875Te), and Cu-doped ZnTe (Zn0.875Cu0.125Te) were optimized using the pseudopotential plane wave (PP-PW) method based on the density functional theory (DFT) within generalized gradient approximation (GGA). The cohesive energy, band structure, density of states, and Mulliken populations were calculated and discussed in detail. On the other hand, an accurate calculation of linear optical functions (the dielectric function, refraction index, reflectivity, conductivity function, and energy-loss spectrum) was performed. The results demonstrated that compared to the perfect ZnTe, the lattice parameters of Zn0.875Te and Zn0.875Cu0.125Te were changed and the cell volumes decreased to some extent due to the vacancy and introduction of impurity. A vacancy acceptor level and an acceptor impurity level were produced in Zn0.875Te and Zn0.875Cu0.125Te, respectively. By comparison, Cu doping in the ZnTe system is relatively stable while the monovacancy system is not.