The electronic structures and optical linear response functions of ZnO are calculated. The relationships between electronic structures and optical properties are investigated by using first-principles based upon the density functional theory. The dielectric functions , reflection spectra ,refractive index and of ZnO dominated by electron inter-band transitions are analyzed interms of the precisely calculated band structure and Conductivity density of state. Furthermore, we analyzed the change of electron structure, bonding and optical properties after doping in comparison with the experimental results. The theoretical results offering theoretical data for the design and application of optoelectronic materials of ZnO. Meanwhile , the calculated results also enable more precise monitoring and controlling during the growth of ZnO material .