The electronic and optical properties of cubic SrHfO3 under the variation of pressures were investigated by first-principles calculation within the framework of generalized gradient approximation (GGA). The calculated equilibrium lattice constant of cubic SrHfO3 is in good agreement with available experimental and theoretical results. The result shows that SrHfO3 is an insulator with an indirect band gap up to 20.00 GPa, along (M - Gamma). While the application of pressure above 20.00 GPa the band gap changes to direct band gap, along (Gamma - Gamma). The band gap increases from 3.80 eV to 4.11 eV with the increase in pressure from 0.00 GPa to 35.00 GPa. In order to understand the optical properties of SrHfO3 perovskite, the dielectric function, optical conductivity and electron energy loss are calculated for photon energy up to 14.00 eV. We have also observed the decrease in static dielectric constant with the increase in energy band gap under pressure. (C) 2016 Published by Elsevier B.V.