The first-principles density-functional theory has been carried out to study the structural, electronic, and optical properties of N-doped orthorhombic SrHfO3. The calculated results show the doping of N substituting for O is most favorable. When the doping of N substituting for Hf(Sr), the impurity energy level of N 2p states is introduced in the forbidden band. When the doping of N substituting for O1(O2), the width of the valence bands increases due to the presence of N 2p states in the top of valence bands. The doping of N resulting in red-shift has been studied by analysing the imaginary part of dielectric function epsilon(2)(omega) of N-doped orthorhombic SrHfO3.