In this article, the lattice constants, band structure and optical characteristics of ZnO wurtzite structure under various pressures were studied using the generalized gradient approximation (GGA) method. This method is based on the functional density (DFT) Theory, according to the first principle. The results show that as the pressure increases and the band gap increases, the lattice constants (a and c) decrease. As the pressure increases, the minimum conduction band will move to a higher energy level, and the maximum valence band will move to a lower energy level, thereby increasing the energy band difference. As the pressure increases, the shape of the optical parameter curve remains almost unchanged, and all peaks move to higher energies. The state density, dielectric function, reflectance and absorption coefficient are also calculated. The overview of the spectrum and optical properties is discussed, including the imaginary part of the dielectric function, reflectance and absorption coefficient of wurtzite-type ZnO under environmental conditions. The optical constants indicate that the phase of ZnO wurtzite structure is transparent. We noticed that our measurements are comparable to those observed in the literature.