First-principles calculations were performed to investigate electronic structure of orthorhombic SrHfO3 under pressure. The optimized lattice parameters of the orthorhombic SrHfO3 at zero pressure are in very good agreement with the available experimental and calculational values. The pressure dependence of band structure, density of states (DOS) and charge densities of orthorhombic SrHfO3 was obtained. When pressure is low (<20 GPa) the minimum indirect band gap of the orthorhombic SrHfO3 is Z-Γ while it is changed to be S-Γ when pressure is high (≥20 GPa). With the increase of pressure, the DOS of orthorhombic SrHfO3 shifts to the lower energy. Charge densities imply that bonding between Hf and O is mainly a covalent bonding and the bonding between Sr and O is mainly an ionic bonding. With the increasing of pressure, the covalent bonding (Hf-O) and the ionic bonding (Sr-O) are enhanced, whereas the ionic interactions (Sr-HfO3) are weakened