The formation energy, the geometric structure, the electronic structure and the optical properties of pure and Si-doped orthorhombic SrHfO3 with Si substituting Hf were studied by the first-principles method using plane-wave ultra-soft pseudo-potential calculation based on density functional theory. The negative formation energy results show the reactions from single elements to Si-doped SrHfO3 are energetically favorable and that Si prefers entering the Hf sites rather than the Sr sites. The calculated equilibrium lattice constants of pure SrHfO3 are in good agreement with previous experimental and theoretical results, and the substitution of Si for Hf results in a decrease in the lattice constants. The band structure indicates the band gap decreases after introduction of Si to Hf site. The Mulliken analysis and charge densities suggest that the Hf-O bond is mainly covalent, and the Sr-O bond is mainly ionic in Si-doped SrHfO3. The dielectric functions, the reflectivity, the absorption coefficient, the refractive index, and the energy-loss spectrum were also calculated to get a better understanding of optical properties of Si-doped SrHfO3