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 ultra-soft pseudo-potential approach of the plane wave based upon the density functional theory. The dielectric functions, reflection spectra, refractive index and extinction coefficient of ZnO dominated by electron inter-band transitions are analyzed in terms of the precisely calculated band structure and density of state. The theoretical results agree well with the experimental value, 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.