Electronic structure and optical properties of Cmcm orthorhombic SrHfO3 were computed, using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory (DFT). The equilibrium lattice parameters of orthorhombic SrHfO3 are in good agreement with experimental values. The band structure, densities of states (DOS) and charge densities of Cmcm orthorhombic SrHfO3 have been obtained. The band structure shows that Cmcm orthorhombic SrHfO3 has direct band gap. The charge densities of Cmcm orthorhombic SrHfO3 indicate that bonding between Hf and O is mainly covalent whereas bonding between Sr and O is mainly ionic. The complex dielectric function, refractive index and absorption coefficient of Cmcm orthorhombic SrHfO3 have been predicted. The imaginary and real parts of the calculated complex dielectric function are close to the experimental measurements.