The perovskite SrHfO3 can be a potential candidate among the high-permittivity materials for gate oxide replacement in future metal-oxide semiconductor field-effect transistor technology. Thin films of SrHfO3 were grown by molecular beam epitaxy and compared with SrTiO3 films. Their optical properties were investigated using spectroscopic ellipsometry and analyzed with respect to their structural properties characterized by x-ray diffractometry, atomic force microscopy, and transmission electron microscopy. A band gap of Eg=6.1±0.1 eV is measured optically, which renders this material better suited for gate dielectric applications than SrTiO3 with Eg∼3.4 eV. At similar equivalent oxide thickness, SrHfO3 also exhibits lower gate leakage current than SrTiO3 does.