The electronic structures of c-HfO2 were calculated by using first-principles ultra-soft preudopotential approach of the plane wave based on the density function theory (DFT). The total density of state and partial density of states as well as the band structure of c-HfO2 were obtained. With band gap correction, the optical linear response functions of c-HfO2 as a function of photon energy were derived including the complex dielectric functions, reflectivity, complex refractive index and optical absorption coefficient. The relationships between optical properties and electronic structures of c-HfO2 were investigated. The calculated results are in agreement with the experimental value and other theoretical results, offering theoretical data for the design and application of optoelectronic materials of c-HfO2. It is also indicated that using DFT generalized gradient approximation (GGA) approach to calculate and predict the electronic structure as well as the optical properties of c-HfO2 is reliable.